a class of preconditioners based on the i s α type preconditioning matrices for solving linear systems abstract the purpose of this paper is to present a class of preconditioners based on the i s type preconditioning matrices provided by evans et al d j evans m m martins m e trigo the aor iterative method for new preconditioned linear systems j comput appl math 132 2001 461 466 and zhang et al y zhang t z huang x p liu modified iterative methods for nonnegative matrices and m matrices linear systems comput math appl 50 2005 1587 1602 three mathematical models are presented to seek the optimal parameter for these preconditioners numerical results are presented which show the improvements on the convergence rate of the jacobi type and gauss seidel type preconditioned iterative methods

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

block gauss elimination followed by a classical iterative method for the solution of linear systems in the last two decades many papers have appeared in which the application of an iterative method for the solution of a linear system is preceded by a step of the gauss elimination process in the hope that this will increase the rates of convergence of the iterative method this combination of methods has been proven successful especially when the matrix a of the system is an m matrix the purpose of this paper is to extend the idea of one to more gauss elimination steps consider other classes of matrices a e g p cyclic consistently ordered and generalize and improve the asymptotic convergence rates of some of the methods known so far

improving jacobi and gauss seidel iterations abstract when convergent jacobi or gauss seidel iterations can be applied to solve systems of linear equations a natural question is how convergence rates are affected if the original system is modified by performing some gaussian elimination we prove that if the initial iteration matrix is nonnegative then such elimination improves convergence our results extend those contained in 4

improving jacobi methods for nonnegative h matrices linear systems abstract in this paper we consider a preconditioned iterative method for solving linear system ax b which is a generalization of method proposed by zhang et al y zhang t z huang x p liu modified iterative methods for nonnegative matrices and m matrices linear systems comput math appl 50 2005 1587 1602 and prove its convergence for the case when a is a nonnegative h matrix numerical examples are also given which show the effectiveness of our method

interpolation with fourier radial adaptive thresholding many interpolation methods are effective with regularly sampled or randomly sampled data whereas the spatial sampling of seismic reflectivity data is typically neither regular nor random fourier radial adaptive thresholding frat is a sparsity promoting method in which the interpolated result is sparse in the frequency wavenumber domain and is coherent in a manner consistent with that of a collection of unaliased plane waves the sparsity and the desired pattern in the f k domain are promoted by iterative soft thresholding and adaptive weighting data in the f k domain are transformed to polar coordinates and then low pass filtered along the radial axis to generate the nonlinear weight frat interpolates data that are randomly sampled and aliased i e where the minimum distance between adjacent traces is greater than the nyquist sampling interval a conventional approach to solving this problem is to apply a cascade of two procedures first a sparsity based method such as projection onto convex sets

convergence of parallel multisplitting iterative methods for m matrices abstract despite the major recent activity in parallel processing few effective new algorithms designed exclusively for multiprocessors have been put forth one such is the multisplitting iterative algorithm suggested by o leary and white although they have given some sufficient conditions for convergence a general convergence theory has not been developed even for the classical situation where the coefficient matrix a is an m matrix or is symmetric positive definite in this paper we study the m matrix case in detail the multisplitting process for a rn n is recast as an ordinary iterative process for a certain block matrix a r kn kn where k is the number of processors and standard convergence results are used to develop a convergence theory for multisplitting iterative methods where a is an m matrix comparison results between multisplitting methods are established in terms of monotonic norms and for the case where a is irreducible in terms of the asymptotic convergence rate a key observation here is that in certain cases the rate of global convergence of these parallel iterative methods is inherent in the splitting of a and is independent of the manner in which the work is distributed among the processors thus in general one can distribute the work for load balancing purposes without affecting the convergence rate

preconditioned gaor methods for solving weighted linear least squares problems in this paper we present the preconditioned generalized accelerated overrelaxation gaor method for solving linear systems based on a class of weighted linear least square problems two kinds of preconditioning are proposed and each one contains three preconditioners we compare the spectral radii of the iteration matrices of the preconditioned and the original methods the comparison results show that the convergence rate of the preconditioned gaor methods is indeed better than the rate of the original method whenever the original method is convergent finally a numerical example is presented in order to confirm these theoretical results

more on modifications and improvements of classical iterative schemes for m matrices in the last four decades many articles have been devoted to the modifications and improvements of classes of preconditioners for linear systems whose matrix coefficient is an m matrix in order to improve on the convergence rates of the classical iterative schemes jacobi gauss seidel etc the present work is a contribution towards the generalization of the most common preconditioners used so far

fourier reconstruction of marine streamer data in four spatial coordinates many methods exist for interpolation of seismic data in one and two spatial dimensions but few can interpolate properly in three or four spatial dimensions marine multi streamer data typically are sampled relatively well in the midpoint and absolute offset coordinates but not in the azimuth because the crossline shot coordinate is significantly under sampled we approach the problem of interpolation of marine streamer data in four spatial dimensions by splitting the problem into a 1d interpolation along the densely sampled streamers and a 3d fourier reconstruction for the remaining spatial coordinates in fourier reconstruction the fourier coefficients that synthesize the nonuniformly sampled seismic data are estimated in a least squares inversion the method is computationally efficient requires no subsurface information and can handle uniform grids with missing data as well as nonuniform grids or random sampling the output grid of the 1d interpolation in the first step is arbitrary when the output grid has uniform inline midpoints spacing the 3d fourier reconstruction in the second step is performed in the crossline midpoint absolute offset and azimuth coordinates when the first step outputs to uniform absolute offset the 3d fourier reconstruction handles the crossline inline midpoint and the azimuth coordinates in both cases the main innovation is the inclusion of the azimuthal coordinate in the fourier reconstruction the azimuth multiplicity must be increased for the method to be successful which means that overlap shooting is required we have tested the algorithm on synthetic streamer data for which the proposed method outperforms an approach where the azimuthal coordinate is ignored potential applications are interpolation of marine streamer data to decrease the crossline source sampling for the benefit of 3d multiple prediction and regularization to reduce sampling related differences in processing of time lapse data

comparison theorems of preconditioned gauss seidel methods for m matrices in this paper a new preconditioner for the gauss seidel method is proposed for solving linear systems whose coefficient matrix is an m matrix several comparison theorems are shown for the proposed method with several preconditioners it follows from the comparison results that our preconditioner is one of the best preconditioners in the sense of convergence rate finally numerical examples are given to illustrate our theoretical results two conjectures are proposed as well based on our numerical tests

letter to the editor comment on a comparison theorem of the sor iterative method in this work we point out that there are incorrect assertions in the article by li ying sun li ying sun a comparison theorem for the sor iterative method j comput appl math 181 2005 336 341 moreover we answer an open problem

green s function representations for seismic interferometry the term seismic interferometry refers to the principle of generating new seismic responses by crosscorrelating seismic observations at different receiver locations the first version of this principle was derived by claerbout 1968 who showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response for an arbitrary 3d inhomogeneous lossless medium it follows from rayleigh s reciprocity theorem and the principle of time reversal invariance that the acoustic green s function between any two points in the medium can be represented by an integral of crosscorrelations of wavefield observations at those two points the integral is along sources on an arbitrarily shaped surface enclosing these points no assumptions are made with respect to the diffusivity of the wavefield the rayleigh betti reciprocity theorem leads to a similar representation of the elastodynamic green s function when a part of the enclosing surface is the earth s free surface the integral needs only to be evaluated over the remaining part of the closed surface in practice not all sources are equally important the main contributions to the reconstructed green s function come from sources at stationary points when the sources emit transient signals a shaping filter can be applied to correct for the differences in source wavelets when the sources are uncorrelated noise sources the representation simplifies to a direct crosscorrelation of wavefield observations at two points similar as in methods that retrieve green s functions from diffuse wavefields in disordered media or in finite media with an irregular bounding surface

improving aor method for consistent linear systems abstract milaszewicz j p milaszewicz improving jacobi and gauss seidel iterations linear algebra appl 93 1987 161 170 and gunawardena et al a d gunawardena s k jain l snyder modified iteration methods for consistent linear systems linear algebra appl 154 156 1991 123 143 presented preconditioned methods for linear system in order to improve the convergence rates of jacobi and gauss seidel iterative schemes respectively in this paper we apply aor and sor iterative schemes to the preconditioned linear systems and provide two theorems to improve the convergence rates of these iterative methods meanwhile the methods in this paper can be used to more class of linear systems

the constraints on images of rectangular polyhedra this paper discusses how polyhedron interpretation techniques are simplified if the objects are rectangular trihedral polyhedra this restriction enables one to compute the spatial orientation of a given corner and its motion from its image in terms of polar coordinates eulerian angles and quaternions one can also interpret the shape and the face adjacency from local information only the necessary constraints are listed and some examples are given to compare the presented scheme to existing ones the possible nonuniqueness of the interpretation is also discussed

on the rate of convergence of the preconditioned conjugate gradient method we derive new estimates for the rate of convergence of the conjugate gradient method by utilizing isolated eigenvalues of parts of the spectrum we present a new generalized version of an incomplete factorization method and compare the derived estimates of the number of iterations with the number actually found for some elliptic difference equations and for a similar problem with a model empirical distribution function

erratum to a note on the preconditioned gauss seidel method for m matrices j comput appl math 219 1 2008 59 71 in this note some errors in a recent article by niki et al h niki t kohno m morimoto the preconditioned gauss seidel method faster than the sor method j comput appl math 219 2008 59 71 are pointed out and a new proof for the corresponding result is presented

convergence of two stage and multisplitting methods using various types of splittings we first study the convergence of both two stage iterative method and multisplitting methods using various types of splittings for solving a linear system whose coefficient matrix is an m matrix or an h matrix we next study a parallel implementation of two stage multisplitting method associated with a special multisplitting and an application of the two stage multisplitting method to parallel preconditioner of krylov subspace methods lastly we provide parallel performance results of both two stage multisplitting method and krylov subspace method with a parallel preconditioner which is derived from two stage multisplitting method on the ibm p690 supercomputer

the convergence of the modified gauss seidel methods for consistent linear systems in this paper we present a convergence analysis for the modified gauss seidel methods given in gunawardena et al linear algebra appl 154 156 1991 125 and kohno et al linear algebra appl 267 1997 113 for consistent linear systems we prove that the modified gauss seidel method converges for some values of the parameters in the preconditioned matrix

comparison results on preconditioned sor type iterative method for z matrices linear systems in this paper we present some comparison theorems on preconditioned iterative method for solving z matrices linear systems comparison results show that the rate of convergence of the gauss seidel type method is faster than the rate of convergence of the sor type iterative method

reconstruction of consistent shape from inconsistent data optimization of 2 raise0 5ex hbox scriptstyle 1 kern 0 1em kern 0 15em lower0 25ex hbox scriptstyle 2 d sketches although the 3d orientations of edges and surfaces are theoretically sufficient for reconstructing the 3d object shape this does not mean that the 3d object shape can actually be reconstructed specifying the edge and surface orientations is often overspecification and inconsistency may result if image data contain errors we propose a scheme of optimization to construct a consistent polyhedron shape from inconsistent data our optimization is achieved by solving a set of linear equations no searchers and iterations are necessary this technique is first applied to the problem of shape from motion and then to the 3d recovery based on the rectangularity hypothesis and the parallelism hypothesis we also present a strategy of heuristic reasoning on rectangularity and parallelism

scheduled relaxation jacobi method elliptic partial differential equations epdes appear in a wide variety of areas of mathematics physics and engineering typically epdes must be solved numerically which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution the scheduled relaxation jacobi srj is a promising class of methods atypical for combining simplicity and efficiency that has been recently introduced for solving linear poisson like epdes the srj methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances the efficiency in the reduction of the residual increases with the number of levels employed in the algorithm applying the original methodology to compute the algorithm parameters with more than 5 levels notably hinders obtaining optimal srj schemes as the mixed non linear algebraic differential system of equations from which they result becomes notably stiff here we present a new methodology for obtaining the parameters of srj schemes that overcomes the limitations of the original algorithm and provide parameters for srj schemes with up to 15 levels and resolutions of up to 215 points per dimension allowing for acceleration factors larger than several hundreds with respect to the jacobi method for typical resolutions and in some high resolution cases close to 1000 most of the success in finding srj optimal schemes with more than 10 levels is based on an analytic reduction of the complexity of the previously mentioned system of equations furthermore we extend the original algorithm to apply it to certain systems of non linear epdes we compute new optimal parameters of the scheduled relaxation jacobi method the new parameters are calculated for srj schemes with p 6 to p 15 levels we reduce the stiffness in the computation of optimal srj parameters analytically we provide a grid of optimal parameters for different p and numerical resolutions we benchmark srj methods against other algorithms to solve linear systems

the aor iterative method for new preconditioned linear systems 461 abstract in this paper we apply the aor method to preconditioned linear systems different from those considered in evans and martins internat j comput math 5 1995 69 76 gunawardena et al linear algebra appl 154 156 1991 123 143 and li and evans technical report no 901 department of computer studies university of loughborough 1994 our results show that some improvements in the convergence rate of this iterative method can be obtained

multidimensional de aliased cadzow reconstruction of seismic records abstractwe tested a strategy for beyond alias interpolation of seismic data using cadzow reconstruction the strategy enables cadzow reconstruction to be used for interpolation of regularly sampled seismic records first in the frequency space f x domain we generated a hankel matrix from the spatial samples of the low frequencies to perform interpolation at a given frequency the spatial samples were interlaced with zero samples and another hankel matrix was generated from the zero interlaced data next the rank reduced eigen decomposition of the hankel matrix at low frequencies was used for beyond alias preconditioning of the hankel matrix at a given frequency finally antidiagonal averaging of the conditioned hankel matrix produced the final interpolated data in addition the multidimensional extension of the proposed algorithm was explained the proposed method provides a unifying thread between reduced rank cadzow reconstruction and beyond alias f x prediction error interpolation synthetic an

interpolation of near offsets using multiples and prediction error filters reflection seismic data typically are undersampled missing near offsets can be interpolated in reflection seismic data with pseudoprimaries generated by crosscorrelating multiples and primaries in incomplete recorded data these pseudoprimary data can be generated at the missing near offsets but contain many artifacts so it is undesirable simply to replace the missing data with the pseudoprimaries a nonstationary prediction error filter pef can instead be estimated from the pseudoprimaries and used to interpolate missing data to produce an interpolated output that is superior to direct substitution of the pseudoprimaries into the missing offsets this approach is applied successfully to 2d synthetic and field data limitations in conventional acquisition geometry limit this approach in 3d which can be illustrated using a synthetic data set

on modified jacobi linear operators abstract by means of successive partial substitutions new fixed point linear equations can be obtained from old ones the jacobi method applied to a system in the sequence thus obtained constitutes a partial gauss seidel method applied to the original one and we analyze the behavior of the sequence of spectral radii of the successive iteration matrices the modified jacobi operators we do this under the assumption that the starting operator is nonnegative with respect to a proper cone and has spectral radius less or greater than 1 our main result is that if the jacobi operator obtained after k substitutions is irreducible then the following one either is the same or has strictly smaller or greater spectral radius this result implies that the whole sequence of spectral radii is monotone

crossline wavefield reconstruction from multicomponent streamer data part 1 multichannel interpolation by matching pursuit mimap using pressure and its crossline gradient we introduce a technique that uses multicomponent seismic measurements to reconstruct the seismic wavefield at any desired crossline position between towed streamers this method called multichannel interpolation by matching pursuit mimap operates on pressure and crossline particle motion measurements it is based on the matching pursuit technique and iteratively reconstructs the signal as a combination of optimal basis functions being a data dependent technique mimap can interpolate severely aliased data without assumptions about seismic events such as linearity or the model related to the seismic wavefield mimap has the capability to perform well in the presence of irregular sampling and is robust when only a small number of samples are available using synthetic data examples we show that the new method has the potential to interpolate signals that are sampled at realistic crossline streamer spacing and in the presence of noise

letter to the editor a note on the preconditioned gauss seidel gs method for linear systems wen li j comput appl math 182 2005 81 90 asserted that there are some errors in article by hiroshi niki kyouji harada munenori morimoto and michio sakakihara j comput appl math 164 165 2004 587 600 and li presented a new proof for the corresponding results in h niki et al in this paper we point out some errors in li s assertion moreover we show that a new proof presented by li is imperfect

beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data we propose a robust interpolation scheme for aliased regularly sampled seismic data that uses the curvelet transform in a first pass the curvelet transform is used to compute the curvelet coefficients of the aliased seismic data the aforementioned coefficients are divided into two groups of scales alias free and alias contaminated scales the alias free curvelet coefficients are upscaled to estimate a mask function that is used to constrain the inversion of the alias contaminated scale coefficients the mask function is incorporated into the inversion via a minimum norm least squares algorithm that determines the curvelet coefficients of the desired alias free data once the alias free coefficients are determined the curvelet synthesis operator is used to reconstruct seismograms at new spatial positions the proposed method can be used to reconstruct regularly and irregularly sampled seismic data we believe that our exposition leads to a clear unifying thread between f x and f k beyond alias interpo

two new modified gauss seidel methods for linear system with m matrices in 2002 h kotakemori et al proposed the modified gauss seidel mgs method for solving the linear system with the preconditioner p i s m a x h kotakemori k harada m morimoto h niki a comparison theorem for the iterative method with the preconditioner i s m a x j comput appl math 145 2002 373 378 since this preconditioner is constructed by only the largest element on each row of the upper triangular part of the coefficient matrix the preconditioning effect is not observed on the nth row in the present paper to deal with this drawback we propose two new preconditioners the convergence and comparison theorems of the modified gauss seidel methods with these two preconditioners for solving the linear system are established the convergence rates of the new proposed preconditioned methods are compared in addition numerical experiments are used to show the effectiveness of the new mgs methods

improvements of preconditioned aor iterative method for l matrices in this paper we improve the preconditioned aor method of linear systems considered by evans et al the aor iterative method for new preconditioned linear systems comput appl math 132 2001 461 466 in evans paper the coefficient matrix of linear system have to be an l matrix with a i i 1a i 1 i 0 i 1 n 1 and 0

a note on the preconditioner pm i sm kotakemori et al h kotakemori k harada m morimoto h niki a comparison theorem for the iterative method with the preconditioner i s m a x journal of computational and applied mathematics 145 2002 373 378 have reported that the convergence rate of the iterative method with a preconditioner p m i s m was superior to one of the modified gauss seidel method under the condition these authors derived a theorem comparing the gauss seidel method with the proposed method however through application of a counter example wen li wen li a note on the preconditioned gaussseidel gs method for linear systems journal of computational and applied mathematics 182 2005 81 91 pointed out that there exists a special matrix that does not satisfy this comparison theorem in this note we analyze the reason why such a to counter example may be produced and propose a preconditioner to overcome this problem

imaging of multiple reflections current multiple removal algorithms in seismic processing use either differential moveout or predictability if the differential moveout between primaries and multiples is small prediction is the only option available in the last decade multidimensional prediction error filtering by weighted convolution such as surface related multiple elimination srme have proved to be very successful in practice so far multiples have been considered as noise and have been discarded after the removal process in this paper we argue that multiple reflections contain a wealth of information that can be used in seismic processing to improve the resolution of reservoir images beyond current capability in the near future one may expect that the so called weighted crosscorrelation wcc concept may offer an attractive alternative in approaching the multiple problem wcc creates an option to avoid the adaptive subtraction process as applied in prediction error algorithms moreover it allows the transformation of multiples into primaries the latter means that seismic imaging with primaries and multiples nonlinear process can be implemented by a sequence of linear processes including the transformation of multiples into primaries and the imaging of primaries

spatial antialias filtering in the slowness frequency domain a rigorous explicit spatial antialias filter is designed and applied to spatially coarsely sampled seismic data by removing all energy above the first nyquist wavenumber and aliased energy that is folded back across the nyquist in the horizontal slowness frequency domain the spatial filtering in the slowness frequency domain is explicit free from any event linearity assumption and does not require any interpolation the spatially aliased energy is dispersive and present at small and large slownesses comparison of the output data after antialias spatial filtering with output data after conventional antialias frequency filtering shows that the filter removes the spatially aliased frequencies selectively at each slowness antialias low pass frequency filtering under or overcorrects for spatial aliasing at all slownesses a seismic gather can be spatially dealiased only at the expense of wavelet spectral changes dealiasing and preservation of amplitude variations with offset are not simultaneously possible

high order sparse radon transform for avo preserving data reconstruction abstractthe sparse radon transform rt represents seismic data by the superposition of a few constant amplitude events and thus it has trouble dealing with amplitude versus offset avo variations we integrated the gradient and curvature parameters of avo into the rt with these additional properties the lateral continuity of the events amplitude was modeled in the transformation and it could be fitted with orthogonal polynomials this resulted in a higher order rt which included avo terms the high order rt is a highly underdetermined problem which was solved by extracting the major model parameters from energy distribution in a high order radon domain and by decreasing the number of inversion parameters thus a high order sparse rt was achieved the proposed method can be used for data interpolation as well as extrapolation the avo preservation performance of the proposed algorithm in data reconstruction was illustrated using both synthetic and field data examples and the results showed the fe

comparison results for solving preconditioned linear systems in this paper we present some comparison theorems between two different modified gauss seidel mgs methods the second preconditioning based on the first preconditioning is also discussed in this paper

gauss type preconditioning techniques for linear systems abstract many researchers have considered preconditioners chosen to eliminate the off diagonal elements of the coefficient matrix of a linear system in this work we generalize the left gauss type preconditioners y zhang t z huang x p liu modified iterative methods for nonnegative matrices and m matrices linear systems comput math appl 50 2005 1587 1602 which eliminate the strictly lower triangular elements right gauss type preconditioners that eliminate strictly upper triangular elements are proposed in this paper these gauss type preconditioners are partly derived from the lu factorization method theoretic analysis on spectral radii of the two kinds of gauss type preconditioners is given numerical experiments are used to show the performance of the improved inbuilt left and right gauss type preconditioning algorithms associated with jacobi type and gauss seidel type iterative methods

some new preconditioned generalized aor methods for generalized least squares problems in this paper we present some new preconditioned gaor methods for solving generalized least squares problems and their comparison results comparison results show that the convergence rates of the new preconditioned gaor methods are better than those of the preconditioned gaor methods presented by zhou et al 2009 19 and wang et al 2013 18 whenever these methods are convergent lastly numerical experiments are provided to confirm the theoretical results

an extended gs method for dense linear systems davey and rosindale k davey i rosindale an iterative solution scheme for systems of boundary element equations internat j numer methods engrg 37 1994 1399 1411 derived the gsor method which uses an upper triangular matrix w in order to solve dense linear systems by applying functional analysis the authors presented an expression for the optimum w moreover davey and bounds k davey s bounds a generalized sor method for dense linear systems of boundary element equations siam j comput 19 1998 953 967 also introduced further interesting results in this note we employ a matrix analysis approach to investigate these schemes and derive theorems that compare these schemes with existing preconditioners for dense linear systems we show that the convergence rate of the gauss seidel method with preconditioner p g is superior to that of the gsor method moreover we define some splittings associated with the iterative schemes some numerical examples are reported to confirm the theoretical analysis we show that the egs method with preconditioner p g c o p t produces an extremely small spectral radius in comparison with the other schemes considered

a comparison theorem for the sor iterative method in 1997 kohno et al have reported numerically that the improving modified gauss seidel method which was referred to as the imgs method is superior to the sor iterative method in this paper we prove that the spectral radius of the imgs method is smaller than that of the sor method and gauss seidel method if the relaxation parameter w 0 1 as a result we prove theoretically that this method is succeeded in improving the convergence of some classical iterative methods some recent results are improved

three dimensional irregular seismic data reconstruction via low rank matrix completion abstractwe have developed a new algorithm for the reconstruction of seismic traces randomly missing from a uniform grid of a 3d seismic volume several algorithms have been developed for such reconstructions based on properties of the seismic wavefields and on signal processing concepts such as sparse signal representation in a transform domain we have investigated a novel approach originally introduced for noise removal which is based on the premise that for suitable representation of the seismic data as matrices or tensors the rank of the seismic data computed by singular value decomposition increases with noise or missing traces thus we apply low rank matrix completion mc with a designed texture patch transformation to 3d seismic data reconstruction low rank components capture geometrically meaningful structures in seismic data that encompass conventional local features such as events and dips the low rank mc is based on nuclear norm minimization an efficient l1 norm minimizing algorithm

f x adaptive seismic trace interpolation we use exponentially weighted recursive least squares to estimate adaptive prediction filters for frequency space f x seismic interpolation adaptive prediction filters can model signals where the dominant wavenumbers vary in space this concept leads to an f x interpolation method that does not require windowing strategies for optimal results in other words adaptive prediction filters can be used to interpolate waveforms that have spatially variant dips the interpolation method s performance depends on two parameters filter length and forgetting factor we pay particular attention to selection of the forgetting factor because it controls the algorithm s adaptability to changes in local dip finally we use synthetic and real data examples to illustrate the performance of the proposed adaptive f x interpolation method

seismic data interpolation beyond aliasing using regularized nonstationary autoregression seismic data are often inadequately or irregularly sampled along spatial axes irregular sampling can produce artifacts in seismic imaging results we present a new approach to interpolate aliased seismic data based on adaptive predictionerror ltering pef and regularized nonstationary autoregression instead of cutting data into overlapping windows patching a popular method for handling nonstationarity we obtain smoothly nonstationary pef coecients by solving a global regularized least squares problem we employ shaping regularization to control the smoothness of adaptive pefs finding the interpolated traces can be treated as another linear least squares problem which solves for data values rather than lter coecients compared with existing methods the advantages of the proposed method include an intuitive selection of regularization parameters and fast iteration convergence benchmark synthetic and eld data examples show that the proposed technique can successfully reconstruct data with decimated or missing traces

seismic trace interpolation in the f x domain interpolation of seismic traces is an effective means of improving migration when the data set exhibits spatial aliasing a major difficulty of standard interpolation methods is that they depend on the degree of reliability with which the various geological events can be separated in this respect a multichannel interpolation method is described which requires neither a priori knowledge of the directions of lateral coherence of the events nor estimation of these directions the method is based on the fact that linear events present in a section made of equally spaced traces may be interpolated exactly regardless of the original spatial interval without any attempt to determine their true dips the predictability of linear events in the f x domain allows the missing traces to be expressed as the output of a linear system the input of which consists of the recorded traces the interpolation operator is obtained by solving a set of linear equations whose coefficients depend only on the spectrum of the spatial prediction filter defined by the recorded traces synthetic examples show that this method is insensitive to random noise and that it correctly handles curvatures and lateral amplitude variations assessment of the method with a real data set shows that the interpolation yields an improved migrated section

convergence of the preconditioned aor method for irreducible l matrices in this paper we first point out some errors in a recent article by li et al y li c li s wu improving aor method for consistent linear systems appl math comput 186 2007 379 388 and then we provide some correct results for convergence of the preconditioned aor method for irreducible l matrices lastly we provide numerical experiments to illustrate the theoretical results

interferometric interpolation of missing seismic data we have developed an interferometric interpolation method for filling in trace gaps in common shot gathers there are two steps for implementation first virtual traces are created in the trace gaps by crosscorrelating recorded traces in a shot gather followed by summing correlated trace pairs over all shot positions second a 1d matching filter is applied to the predicted events to correct for wavelet and amplitude distortions by using a 1d assumption assuming a layered medium around the midpoint in a common midpoint cmp gather the interferometric interpolation method can be applied to cmp gathers it is a fully data driven method that requires only the original data results with synthetic and field data empirically show that the near offset traces can be interpolated but because of the approximations introduced by a limited recording aperture there are still some artifacts for comparison a 2d nonstationary prediction error filter pef was also used instead of a 1d matching filter in the se

three dimensional realization of anomalous pictures an application of picture interpretation theory to toy design anomalous pictures are naively regarded as pictures of impossible objects but some of them are realizable as three dimensional polyhedral objects this paper presents an interactive system for generating the unfolded surfaces of those objects thus offering toy material from which children can make impossible objects

accelerated iterative method for z matrices it has recently been reported that the convergence of the preconditioned gauss seidel method which uses a matrix of the type i u as a preconditioner is faster than the basic iterative method in this paper we generalize the preconditioner to the type i bu where b is a positive real number after discussing convergence of the method applied to z matrices we propose an algorithm for estimating the optimum b numerical examples are also given which show the effectiveness of our algorithm

study on the preconditioners i sm kotakemori et al 2002 2 have reported that the convergence rate of the iterative method with a preconditioner p m i s m a x was superior to one of the modified gauss seidel methods under a special condition the authors derived a theorem comparing the gauss seidel method to remove the requirement for this condition morimoto et al 2004 4 have proposed the preconditioner p s m i s s m however it is pointed out that there exists a special matrix that does not satisfy this comparison theorem to overcome this problem kohno et al 2009 3 have proposed some preconditioners in this note we present a new preconditioner and from numerical results we show that the convergence rate of the proposed method is better than that of the gauss seidel method with other preconditioners in addition we presented the comparison theorem for the proposed preconditioner we succeeded to overcome two drawbacks mentioned above

minimum weighted norm interpolation of seismic records in seismic data processing we often need to interpolate and extrapolate data at missing spatial locations the reconstruction problem can be posed as an inverse problem where from inadequate and incomplete data we attempt to reconstruct the seismic wavefield at locations where measurements were not acquired we propose a wavefield reconstruction scheme for spatially band limited signals the method entails solving an inverse problem where a wavenumber domain regularization term is included the regularization term constrains the solution to be spatially band limited and imposes a prior spectral shape the numerical algorithm is quite efficient since the method of conjugate gradients in conjunction with fast matrix vector multiplications implemented via the fast fourier transform fft is adopted the algorithm can be used to perform multidimensional reconstruction in any spatial domain

lu decomposition of m matrices by elimination without pivoting abstract it is shown that if a or a is a singular m matrix satisfying the generalized diagonal dominance condition y t a 0 for some vector y 0 then a can be factored into a lu by a certain elimination algorithm where l is a lower triangular m matrix with unit diagonal and u is an upper triangular m matrix the existence of lu decomposition of symmetric permutations of a and for irreducible m matrices and symmetric m matrices follow as colollaries this work is motivated by applications to the solution of homogeneous systems of linear equations ax 0 where a or a is an m matrix these applications arise e g in the analysis of markov chains input output economic models and compartmental systems a converse of the theorem metioned above can be established by considering the reduced normal form of a

a comparison theorem for the iterative method with the preconditioner i s max in 1991 gunawardena et al linear algebra appl 154 156 1991 123 have reported the modified gauss seidel method with a preconditioner i s in this article we propose to use a preconditioner i smax instead of i s here smax is constructed by only the largest element at each row of the upper triangular part of a by using the lemma established neumann and plemmons linear algebra appl 88 89 1987 559 we get the comparison theorem for the proposed method simple numerical examples are also given

improving the modified gauss seidel method for z matrices abstract in 1991 a d gunawardena et al reported that the convergence rate of the gauss seidel method with a preconditioning matrix i s is superior to that of the basic iterative method in this paper we use the preconditioning matrix i s if a coefficient matrix a is an irreducibly diagonally dominant z matrix then i s a is also a strictly diagonally dominant z matrix it is shown that the proposed method is also superior to other iterative methods

modified iterative methods for consistent linear systems abstract in order to solve a linear system ax b certain elementary row operations are performed on a before applying the gauss seidel or jacobi iterative methods it is shown that when a is a nonsingular m matrix or a singular tridiagonal m matrix the modified method yields considerable improvement in the rate of convergence for the iterative method it is also shown that in some cases this method is superior to certain other modified iterative methods the performance of this modified method on some matrices other than m matrices is also investigated

recognition of polyhedral objects using triplets of projected spatial edges based on a single perspective image abstract a novel and intuitive mathematical formulation is proposed for the interpretation of the geometric relationships of a triple of spatial edges and their perspective projection forming image lines no restriction is imposed on the configuration of the triple of spatial edges an eighth degree polynomial equation explicitly defined by the space angles between the corresponding three spatial edges in an object frame is derived the crux of this representation is that the angular attributes of pairs of spatial edges are expressed in an object independent coordinate system an effective hypothesis generation scheme is proposed which can take advantage of the representation in the proposed recognition framework triples of connected spatial edges and trihedral vertices are employed as key features for model invocation hypothesis generation and pose estimation extensive experiments are performed to verify the plausibility and robustness of the proposed recognition methods in general the success rate for identifying and localising polyhedral objects using the proposed recognition method is relatively high

the preconditioned gauss seidel method faster than the sor method in recent years a number of preconditioners have been applied to linear systems a d gunawardena s k jain l snyder modified iterative methods for consistent linear systems linear algebra appl 154 156 1991 123 143 t kohno h kotakemori h niki m usui improving modified gauss seidel method for z matrices linear algebra appl 267 1997 113 123 h kotakemori k harada m morimoto h niki a comparison theorem for the iterative method with the preconditioner i s m a x j comput appl math 145 2002 373 378 h kotakemori h niki n okamoto accelerated iteration method for z matrices j comput appl math 75 1996 87 97 m usui h niki t kohno adaptive gauss seidel method for linear systems internat j comput math 51 1994 119 125 10 since these preconditioners are constructed from the elements of the upper triangular part of the coefficient matrix the preconditioning effect is not observed on the nth row of matrix a in the present paper in order to deal with this drawback we propose a new preconditioner in addition the convergence and comparison theorems of the proposed method are established simple numerical examples are also given and we show that the convergence rate of the proposed method is better than that of the optimum sor

preconditioned aor iterative methods for m matrices linear systems with m matrices often appear in a wide variety of areas in this paper we give general preconditioners for solving the systems with nonsingular m matrix we show that our preconditioners increase the convergence rate of aor iterative methods numerical results for corresponding preconditioned gmres methods are also given

numerical shape from shading and occluding boundaries an iterative method for computing shape from shading using occluding boundary information is proposed some applications of this method are shown we employ the stereographic plane to express the orientations of surface patches rather than the more commonly used gradient space use of the stereographic plane makes it possible to incorporate occluding boundary information but forces us to employ a smoothness constraint different from the one previously proposed the new constraint follows directly from a particular definition of surface smoothness we solve the set of equations arising from the smoothness constraints and the image irradiance equation iteratively using occluding boundary information to supply boundary conditions good initial values are found at certain points to help reduce the number of iterations required to reach a reasonable solution numerical experiments show that the method is effective and robust finally we analyze scanning electron microscope sem pictures using this method other applications are also proposed

modified gauss seidel type methods and jacobi type methods for z matrices abstract in this paper we present the convergence analysis for some modified gauss seidel and jacobi type iterative methods and provide a comparison of spectral radius among the gauss seidel iterative method and these modified methods some recent results are improved

a note on the improving modified gauss seidel imgs method abstract in this paper we first provide another proof for a theorem given by sun l sun a comparison theorem for the sor iterative method j comput appl math 181 2005 336 341 by showing that spectral radius of the gauss seidel method is not greater than that of the sor method when 0 1 next convergence results of the imgs method for both an h matrix and a symmetric positive definite matrix are provided

theorems on m splittings of a singular m matrix which depend on graph structure abstract let a m ne r n n be a splitting we investigate the spectral properties of the iteration matrix m 1n by considering the relationships of the graphs of a m n and m 1n we call a splitting an m splitting if m is a nonsingular m matrix and n 0 for an m splitting of an irreducible z matrix a we prove that the circuit index of m 1n is the greatest common divisor of certain sets of integers associated with the circuits of a for m splittings of a reducible singular m matrix we show that the spectral radius of the iteration matrix is 1 and that its multiplicity and index are independent of the splitting these results hold under somewhat weaker assumptions

modified iterative methods for nonnegative matrices and m matrices linear systems the purpose of this paper is to present new preconditioning techniques for solving nonnegative matrices linear system and m matrices linear system ax b based on the i s a type preconditioning matrices provided by hadjidimos et al 1 and evans et al 2 convergence analysis of the proposed methods are given numerical results are presented which show the improvements on the convergence rate of the jacobi type and gauss seidel type preconditioned iterative methods

on optimal improvements of classical iterative schemes for z matrices many researchers have considered preconditioners applied to linear systems whose matrix coefficient is a z or an m matrix that make the associated jacobi and gauss seidel methods converge asymptotically faster than the unpreconditioned ones such preconditioners are chosen so that they eliminate the off diagonal elements of the same column or the elements of the first upper diagonal milaszewicz laa 93 1987 161 170 gunawardena et al laa 154 156 1991 123 143 in this work we generalize the previous preconditioners to obtain optimal methods good jacobi and gauss seidel algorithms are given and preconditioners that eliminate more than one entry per row are also proposed and analyzed moreover the behavior of the above preconditioners to the krylov subspace methods is studied

comparison theorems for weak splittings of bounded operators comparison theorems for weak splittings of bounded operators are presented these theorems extend the classical comparison theorem for regular splittings of matrices by varga the less known result by wo nicki and the recent results for regular and weak regular splittings of matrices by neumann and plemmons elsner and lanzkron rose and szyld the hypotheses of the theorems presented here are weaker and the theorems hold for general banach spaces and rather general cones hypotheses are given which provide strict inequalities for the comparisons it is also shown that the comparison theorem by alefeld and volkmann applies exclusively to monotone sequences of iterates and is not equivalent to the comparison of the spectral radius of the iteration operators

comparison results of the preconditioned aor methods for l matrices abstract in this paper we first provide comparison results of several types of the preconditioned aor paor methods for solving a linear system whose coefficient matrix is an l matrix satisfying some weaker conditions than those used in the recent literature next we propose an application of paor method to a preconditioner of krylov subspace method lastly numerical results are provided to show that krylov subspace method with the paor preconditioner performs quite well as compared with the ilu 0 preconditioner

model based interferometric interpolation method we have proposed a two stage model based interferometric interpolation method for filling in gaps in marine seismic data the first stage is creating virtual traces and the second stage is utilizing modified virtual traces for interpolation there are three steps for creating a virtual trace first set the virtual trace s source and receiver coordinates and retrieve two common receiver gathers crg from existing data at least one crg should be obtained otherwise our method cannot be performed second if only one crg is obtained then a synthetic crg should be generated using known velocity model e g water layer model third the virtual trace is created by summing correlated trace pairs over all identical source positions in two crgs when all virtual traces are created a least squares matching filter or a nonstationary prediction error filter pef should be used together with virtual traces to do the interpolation if the trace gap is small or the subsurface geology is simple the local match

detection of surface orientation and motion from texture by a stereoogical technique abstract a new approach is given to detect the surface orientation and motion from the texture on the surface by making use of a mathematical principle called stereology information about the surface orientation is contained in features computed by scanning the image by parallel lines and counting the number of intersections with the curves of the texture a synthetic example is given to illustrate the technique this scheme can also detect surface motions relative to the viewer by computing features of its texture at one time and a short time later the motion is specified by explicit formulae of the computed features

convergence analysis of the preconditioned gauss seidel method for h matrices in 1997 kohno et al toshiyuki kohno hisashi kotakemori hiroshi niki improving the modified gauss seidel method for z matrices linear algebra appl 267 1997 113 123 proved that the convergence rate of the preconditioned gauss seidel method for irreducibly diagonally dominant z matrices with a preconditioner i s a is superior to that of the basic iterative method in this paper we present a new preconditioner i k b which is different from the preconditioner given by kohno et al toshiyuki kohno hisashi kotakemori hiroshi niki improving the modified gauss seidel method for z matrices linear algebra appl 267 1997 113 123 and prove the convergence theory about two preconditioned iterative methods when the coefficient matrix is an h matrix meanwhile two novel sufficient conditions for guaranteeing the convergence of the preconditioned iterative methods are given

a note on the preconditioned gauss seidal gs method for linear systems in this note recent comparison results for preconditioned gauss seidel gs methods are discussed a new strict comparison result between two different preconditioned gs methods is given some errors in a recent article by niki et al j comput appl math 164 165 2004 587 are pointed out and a new proof for the corresponding results in niki et al is presented

3d interpolation of irregular data with a pocs algorithm seismic surveys generally have irregular areas where data cannot be acquired these data should often be interpolated a projection onto convex sets pocs algorithm using fourier transforms allows interpolation of irregularly populated grids of seismic data with a simple iterative method that produces high quality results the original 2d image restoration method the gerchberg saxton algorithm is extended easily to higher dimensions and the 3d version of the process used here produces much better interpolations than typical 2d methods the only parameter that makes a substantial difference in the results is the number of iterations used and this number can be overestimated without degrading the quality of the results this simplicity is a significant advantage because it relieves the user of extensive parameter testing although the cost of the algorithm is several times the cost of typical 2d methods the method is easily parallelized and still completely practical

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions

the survey of preconditioners used for accelerating the rate of convergence in the gauss seidel method several preconditioned iterative methods reported in the literature have been used for improving the convergence rate of the gauss seidel method in this article on the basis of nonnegative matrix comparisons between some splittings for such preconditioned matrices are derived simple numerical examples are also given

convergence analysis of the two preconditioned iterative methods for m matrix linear systems in this paper we present the two preconditioners i s and i s r for solving m matrix linear systems and discuss the convergence of the two preconditioned iterative methods meanwhile we obtain comparison theorems between the two preconditioned iterative methods and consider the solution of m matrix linear systems by preconditioned krylov subspace methods numerical experiments are given to validate the performance of the preconditioners