shift orthogonal space time block codes in this paper we present a new class of spacetime block code called shift orthogonal space time block codes sostbc which can maintain orthogonality hence symbolwise linear decoding in asynchronous wireless relay networks under both amplify and forward af and decode and forward df relaying schemes the definitions systematic constructions and properties of sostbc are presented we also present some simulation results to illustrate its effectiveness in achieving full asynchronous cooperative diversity

a wavefront based gaussian beam method for computing high frequency wave propagation problems we present a novel wavefront method based on gaussian beams for computing high frequency wave propagation problems unlike standard geometrical optics gaussian beams compute the correct solution of the wave field also at caustics the method tracks a front of two canonical beams with two particular initial values for width and curvature in a fast post processing step from the canonical solutions we recreate any other gaussian beam with arbitrary initial data on the initial front this provides a simple mechanism to include a variety of optimization processes including error minimization and beam width minimization for a posteriori selection of optimal beam initial parameters the performance of the method is illustrated with two numerical examples

rigorous sensitivity analysis for parameter dependent systems of equations abstract in this paper we construct rigorous and realistic enclosures for the solutions of parameter dependent systems of equations f x t 0 the enclosure of the solution x x t is given in the form x 0 s t t 0 with interval vectors x0 t0 and an interval matrix s this allows a detailed analysis of the sensitivity of the solution x t to small changes of t and the influence of specific changes in selected parameters on the solution the linear case is treated separately

high rate single symbol ml decodable precoded dstbcs for cooperative networks distributed orthogonal space time block codes dostbcs achieving full diversity order and single symbol maximum likelihood ml decodability have been introduced recently by yi and kim for cooperative networks and an upper bound on the maximal rate of such codes along with code constructions has been presented in this paper a new class of single symbol ml decodable precoded distributed space time block codes ssd pdstbcs called semiorthogonal ssd pdstbcs semi ssd pdstbcs is introduced wherein the source performs linear precoding of information symbols appropriately before transmitting it to all the relays it is shown that dostbcs are a special case of semi ssd pdstbcs a special class of semi ssd pdstbcs having diagonal covariance matrix at the destination is studied and an upper bound on the maximal rate of such codes is derived the bounds obtained are approximately twice larger than that of the dostbcs a systematic construction of semi ssd pdstbcs is presented when the number of relays k ges 4 the constructed codes are shown to achieve the upper bound on the rate when k is of the form 0 or 3 modulo 4 for the rest of the values of k the constructed codes are shown to have rates higher than that of dostbcs it is shown that semi ssd pdstbcs cannot be constructed with any form of linear processing at the relays when the source does not perform linear precoding of the information symbols

shift full rank matrices and applications in space time trellis codes for relay networks with asynchronous cooperative diversity to achieve full cooperative diversity in a relay network most of the existing space time coding schemes require the synchronization between terminals a family of space time trellis codes that achieve full cooperative diversity order without the assumption of synchronization has been recently proposed the family is based on the stack construction by hammons and el gamal and its generalizations by lu and kumar it has been shown that the construction of such a family is equivalent to the construction of binary matrices that have full row rank no matter how their rows are shifted where a row corresponds to a terminal or transmit antenna and its length corresponds to the memory size of the trellis code on that terminal we call such matrices as shift full rank sfr matrices a family of sfr matrices has been also constructed but the memory sizes of the corresponding space time trellis codes the number of columns of sfr matrices grow exponentially in terms of the number of terminals the number of rows of sfr matrices which may cause a high decoding complexity when the number of terminals is not small in this paper we systematically study and construct sfr matrices of any sizes for any number of terminals furthermore we construct shortest square sfr ssfr matrices that correspond to space time trellis codes with the smallest memory sizes and asynchronous full cooperative diversity we also present some simulation results to illustrate the performances of the space time trellis codes associated with sfr matrices in asynchronous cooperative communications

convergence of frozen gaussian approximation for high frequency wave propagation the frozen gaussian approximation provides a highly efficient computational method for high frequency wave propagation the derivation of the method is based on asymptotic analysis in this paper for general linear strictly hyperbolic systems we establish the rigorous convergence result for frozen gaussian approximation as a byproduct higher order frozen gaussian approximation is developed 2011 wiley periodicals inc

single symbol ml decodable distributed stbcs for cooperative networks in this correspondence the distributed orthogonal space time block codes dostbcs which achieve the single symbol maximum likelihood ml decodability and full diversity order are first considered however systematic construction of the dostbcs is very hard since the noise covariance matrix is not diagonal in general thus some special dostbcs which have diagonal noise covariance matrices at the destination terminal are investigated these codes are referred to as the row monomial dostbcs an upper bound of the data rate of the row monomial dostbc is derived and it is approximately twice higher than that of the repetition based cooperative strategy furthermore systematic construction methods of the row monomial dostbcs achieving the upper bound of the data rate are developed when the number of relays and or the number of information bearing symbols are even

gaussian beam decomposition of high frequency wave fields in this paper we present a method of decomposing a highly oscillatory wave field into a sparse superposition of gaussian beams the goal is to extract the necessary parameters for a gaussian beam superposition from this wave field so that further evolution of the high frequency waves can be computed by the method of gaussian beams the methodology is described for r d with numerical examples for d 2 in the first example a field generated by an interface reflection of gaussian beams is decomposed into a superposition of gaussian beams the beam parameters are reconstructed to a very high accuracy the data in the second example is not a superposition of a finite number of gaussian beams the wave field to be approximated is generated by a finite difference method for a geometry with two slits the accuracy in the decomposition increases monotonically with the number of beams

analysis of high order fast interface tracking methods fast high order methods for the propagation of an interface in a velocity field are constructed and analyzed the methods are generalizations of the fast interface tracking method proposed in runborg commun math sci 7 365 398 2009 they are based on high order subdivision to make a multiresolution decomposition of the interface instead of tracking marker points on the interface the related wavelet vectors are tracked like the markers they satisfy ordinary differential equations odes but fine scale wavelets can be tracked with longer timesteps than coarse scale wavelets this leads to methods with a computational cost of o log n delta t o log n t rather than o n delta t o n t for n n markers and reference timestep delta t t these methods are proved to still have the same order of accuracy as the underlying direct ode solver under a stability condition in terms of the order of the subdivision the order of the ode solver and the time step ratio between wavelet levels in particular it is shown that with a suitable high order subdivision scheme any explicit runge kutta method can be used numerical examples supporting the theory are also presented

a quadratically convergent krawczyk like algorithm in this paper we introduce a method for computing a solution of a nonlinear system which is similar to that proposed by r krawczyk computing 4 1969 pp 187 201 our method however needs considerably less work per step starting with an interval vector we give a criterion under which the method is convergent to the solution of the system if a solution is contained in the interval vector if the starting vector contains no solution then the method will break down after a finite number of steps

an improved interval newton operator abstract in this paper interval operators producing a sequence of intervals are discussed each interval of such a sequence encloses a set of solutions of nonlinear systems of equations for these interval operators we formulate theorems about existence and uniqueness of fixintervals

space time block codes a maximum snr approach in tarokh et al 1999 space time block codes were introduced to obtain coded diversity for a multiple antenna communication system in this work we cast space time codes in an optimal signal to noise ratio snr framework and show that they achieve the maximum snr and in fact they correspond to a generalized maximal ratio combiner the maximum snr framework also helps in calculating the distribution of the snr and in deriving explicit expressions for bit error rates we bring out the connection between the theory of amicable orthogonal designs and space time codes based on this we give a much simpler proof to one of the main theorems on space time codes for complex symbols we present a rate 1 2 code for complex symbols which has a smaller delay than the code already known we also present another rate 3 4 code which is simpler than the one already known in the sense it does not involve additions or multiplications we also point out the connection between generalized real designs and generalized orthogonal designs

systems of linear interval equations this paper presents theory and methods for computing the exact bounds on the solution of a system of n linear equations in n variables whose coefficients and right hand sides vary in some real intervals finite and iterative methods are given based on results from linear complementarity theory also regularity conditions regularity testing and computing the exact inverse of an interval matrix are dealt with

eulerian gaussian beams for high frequency wave propagation we design an eulerian gaussian beam summation method for solving helmholtz equations in the high frequency regime the traditional gaussian beam summation method is based on lagrangian ray tracing and local ray centered coordinates we propose a new eulerian formulation of gaussian beam theory which adopts global cartesian coordinates level sets and liouville equations yielding uniformly distributed eulerian traveltimes and amplitudes in phase space simultaneously for multiple sources the time harmonic wavefield can be constructed by summing up gaussian beams with ingredients provided by the new eulerian formulation the conventional gaussian beam summation method can be derived from the proposed method there are three advantages of the new method 1 we have uniform resolution of ray distribution 2 we can obtain wavefields excited at different sources by varying only source locations in the summation formula 3 we can obtain wavefields excited at different frequencies by varying only frequencies in the summation formula numerical experiments indicate that the gaussian beam summation method yields accurate asymptotic wavefields even at caustics the new method may be used for seismic modeling and migration

new techniques for the analysis of linear interval equations abstract the basic properties of interval matrix multiplication and several well known solution algorithms for linear interval equations are abstracted by the concept of a sublinear map the new concept coupled with a systematic use of ostrowski s comparison operator in a form generalized to interval matrices is used to derive quantitative information about the result of interval gauss elimination andthe limit of various iterative schemes for the solution of linear interval equations moreover optimality results are prove for 1 the use of the midpoint inverse as a preconditioning matrix and 2 gauss seidel iteration with componentwise intersection this extends and improves results by scheu krawczyk and alefeld and herzberger

traveltime and amplitude estimation using wavefront construction we have developed and implemented a new method for estimating traveltimes and amplitudes in a general smooth two dimensional 2 d model the basic idea of this wavefront wf construction approach is to use ray tracing to estimate a new wf from the old one the wf is defined as a curve in 2 d of constant traveltime from the source the ray direction and amplitude will then be a function of s the distance along the front to maintain a sufficiently small sampling distance along the wf it is scanned at every time step and new rays are interpolated whenever the distance between two rays becomes larger than a predefined limit as the wavefronts are constructed the data i e traveltimes amplitude coefficients etc are transferred to the receivers by interpolation within the ray cells advantages of the wf construction method are its flexibility robustness and accuracy first second and later arrivals may be found at any point in the model any shape of the initial wavefront is possible the drawb

the cholesky method for interval data abstract we apply the well known cholesky method to bound the solutions of linear systems with symmetric matrices and right hand sides both of which are varying within given intervals we derive criteria to guarantee the feasibility and the optimality of the method furthermore we discuss some general properties

interval slopes for rational functions and associated centered forms for an arithmetic expression f x involving n rational operations an o n algorithm is given which computes an interval enclosure for the set of slopes f x z where x ranges over an interval x applications to real and complex centered forms are given resulting in improvements over previous results by ratschek siam j numer anal 17 1980 pp 656 662 and petkovic freiburger intervall berichte 83 2 1983 pp 33 50

comparison theorems for iterative methods based on strong splittings by means of strong splittings of an n times n interval m matrix mathcal a one can construct iterative methods to enclose the solution set x x ax b a in a b in mathfrak b where mathfrak b is an interval vector and x in mathbb r n we derive comparison theorems for an upper bound of the asymptotic convergence factor and for the fixpoints resulting from those methods

results concerning interval linear systems with multiple right hand sides and the interval matrix equation ax b this note tries to study different solution sets of the interval linear matrix equation ax b where a is a known square interval matrix of dimension mxm b is a rectangular interval matrix of dimension mxn while the unknown matrix x is also of dimension mxn firstly we show that shary s results for interval linear systems with a single right hand side vector cannot be simply generalized to the case of interval linear systems of the form ax b secondly we give some analytical characterizations of the ae solution sets of this interval matrix equation we use a linear programming method in order to find the interval hull matrix on the other hand we propose the use of an interval gaussian elimination to find an enclosure for the united solution set of this matrix equation since the lu decomposition of a is needed only once numerical examples have also been given

on interval operators obtained by splitting the lipschitz matrix abstract interval operators of a function strip obtained by splitting the given lipschitz matrix a b c are discussed using these operators we can construct a sequence of intervals which converges to a limit interval if the set of solutions of a given function strip is not empty under certain conditions the limit interval is a fixed interval of the corresponding interval operator the different fixed intervals and convergence factors for some splittings are determined

on the r order of newton like methods for enclosing solutions of nonlinear equations a class of newton like methods for enclosing solutions of nonlinear equations is considered given q in 1 2 criteria that yield an r order of convergence of at least q are derived in particular it is shown that under certain circumstances this r order can reach 2 the results are illustrated on a discretized version of chandrasekhar s h equation

error estimates for gaussian beam superpositions gaussian beams are asymptotically valid high frequency solutions to hyperbolic partial differential equations concentrated on a single curve through the physical domain they can also be extended to some dispersive wave equations such as the schrodinger equation superpositions of gaussian beams provide a powerful tool to generate more general high frequency solutions that are not necessarily concentrated on a single curve this work is concerned with the accuracy of gaussian beam superpositions in terms of the wavelength epsilon we present a systematic construction of gaussian beam superpositions for all strictly hyperbolic and schrodinger equations subject to highly oscillatory initial data of the form ae i phi epsilon through a careful estimate of an oscillatory integral operator we prove that the k th order gaussian beam superposition converges to the original wave field at a rate proportional to epsilon k 2 in the appropriate norm dictated by the well posedness estimate in particular we prove that the gaussian beam superposition converges at this rate for the acoustic wave equation in the standard epsilon scaled energy norm and for the schrodinger equation in the l 2 norm the obtained results are valid for any number of spatial dimensions and are unaffected by the presence of caustics we present a numerical study of convergence for the constant coefficient acoustic wave equation in r 2 to analyze the sharpness of the theoretical results

a fuzzy approach to markov decision processes with uncertain transition probabilities in this paper markov decision models with uncertain transition matrices which allow a matrix to fluctuate at each step in time is described by the use of fuzzy sets we find a pareto optimal policy maximizing the infinite horizon fuzzy expected discounted reward fedr over all stationary policies under some partial order the pareto optimal policies are characterized by maximal solutions of an optimal inclusion including efficient set functions as a numerical example a machine maintenance problem is considered

prestack gaussian beam depth migration kirchhoff migration is the most popular method of three dimensional prestack depth migration because of its flexibility and efficiency its effectiveness can become limited however when complex velocity structure causes multipathing of seismic energy an alternative is gaussian beam migration which is an extension of kirchhoff migration that overcomes many of the problems caused by multipathing unlike first arrival and most energetic arrival methods which retain only one traveltime this alternative method retains most arrivals by the superposition of gaussian beams this paper presents a prestack gaussian beam migration method that operates on common offset gathers the method is efficient because the computation of beam superposition isolates summations that do not depend on the seismic data and evaluates these integrals by considering their saddle points gaussian beam migration of the two dimensional marmousi test data set demonstrates the method s effectiveness for structural imaging in a case w

overestimation in linear interval equations bounds are given for the overestimation of the solution set of a system of linear interval equations by various inclusion intervals for this set in particular a theorem of gay this journal 19 1982 pp 858 870 on the quadratic approximation property of the preconditioned fixpoint inverse is strengthened

a comparison of some methods for solving linear interval equations certain cases in which the interval hull of a system of linear interval equations can be computed inexpensively are outlined we extend a proposed technique of hansen and rohn with a formula that bounds the solution set of a system of equations whose coefficient matrix bf a underline a overline a is an h matrix when bf a is centered about a diagonal matrix these bounds are the smallest possible i e the bounds are then the solution hull hansen s scheme also computes the solution hull when the linear interval system bf a bf x bf b underline b overline b is such that bf a is inverse positive and underline b overline b neq 0 earlier results of others also imply that when bf a is an m matrix and bf b geq 0 bf b leq 0 or 0 in bf b interval gaussian elimination iga computes the hull we also give a method of computing the solution hull inexpensively in many instances when bf a is inverse positive given an outer approximation such as that obtained from iga examples are used to compare these schemes under various conditions

asynchronous two stage iterative methods parallel block two stage iterative methods for the solution of linear systems of algebraic equations are studied convergence is shown for monotone matrices and for h matrices two different asynchronous versions of these methods are considered and their convergence investigated

nonlinear equations and optimization abstract interval analysis has led to improved numerical algorithms both for the solution of nonlinear equations and for nonlinear optimization in fact interval analysis has made possible algorithms for solving a problem often predicted to be numerically insoluble the nonlinear global optimization problem in this paper we survey interval methods for solving nonlinear equations and optimization

gaussian beam decomposition of high frequency wave fields using expectation maximization a new numerical method for approximating highly oscillatory wave fields as a superposition of gaussian beams is presented the method estimates the number of beams and their parameters automatically this is achieved by an expectation maximization algorithm that fits real positive gaussians to the energy of the highly oscillatory wave fields and its fourier transform beam parameters are further refined by an optimization procedure that minimizes the difference between the gaussian beam superposition and the highly oscillatory wave field in the energy norm

solving systems of linear fuzzy equations by parametric functions buckley and qu proposed a method to solve systems of linear fuzzy equations basically in their method the solutions of all systems of linear crisp equations formed by the alpha levels are calculated we propose in this paper a new method for solving systems of linear fuzzy equations based on a practical algorithm using parametric functions in which the variables are given by the fuzzy coefficients of the system we show that our algorithm is much more efficient than the method of buckley and qu

controlled markov set chains under average criteria in this paper applying an interval arithmetic analysis we consider the average case of controlled markov set chains whose process allows for fluctuating transition matrices at each step in time we introduce a v step contractive property for the average case under which a pareto optimal periodic policy is characterized as a maximal solution of optimality equation also in the class of stationary policies the behavior of the expected reward over t horizon as t approaches is investigated and the left and right hand side optimality equations are given by which a pareto optimal stationary policy is found as a numerical example the taxicab problem is considered

eulerian gaussian beams for schrodinger equations in the semi classical regime we propose gaussian beam based eulerian methods to compute semi classical solutions of the schrodinger equation traditional gaussian beam type methods for the schrodinger equation are based on the lagrangian ray tracing based on the first eulerian gaussian beam framework proposed in leung et al s leung j qian r burridge eulerian gaussian beams for high frequency wave propagation geophysics 72 2007 sm61 sm76 we develop a new eulerian gaussian beam method which uses global cartesian coordinates level set based implicit representation and liouville equations the resulting method gives uniformly distributed phases and amplitudes in phase space simultaneously to obtain semi classical solutions to the schrodinger equation with different initial wave functions we only need to slightly modify the summation formula this yields a very efficient method for computing semi classical solutions to the schrodinger equation for instance in the one dimensional case the proposed algorithm requires only o snm2 operations to compute s different solutions with s different initial wave functions under the influence of the same potential where n o 1 is the planck constant and m n is the number of computed beams which depends on weakly numerical experiments indicate that this eulerian gaussian beam approach yields accurate semi classical solutions even at caustics

further results on linear interval equations abstract as a continuation of my paper new techniques for the analysis of linear interval equations linear algebra appl 58 273 325 1984 the interrelation between interval gauss elimination and interval iteration is investigated main results are a new existence theorem for interval gauss elimination in the guise of a perturbation theorem a convergence and comparison theorem for a general family of interval iteration schemes and a new method for the calculation of the hull of the solution set of linear interval equations with inverse positive coefficient matrix

an interval arithmetic domain decomposition method for a class of elliptic pdes on nonrectangular domains abstract we introduce an interval arithmetic domain decomposition method for linear systems with interval coefficients resulting from the application of difference methods for a class of elliptic boundary value problems on domains with irregular geometry the efficient treatment of such systems is crucial for the efficiency of globally convergent newton like interval methods for the corresponding nonlinear problems

on a theorem of stein rosenberg type in interval analysis in classical numerical analysis the asymptotic convergence factor r1 factor of an iterative processxm 1 axm b coincides with the spectral radius of then n iteration matrixa thus the famous theorem of stein and rosenberg can at least be partly reformulated in terms of asymptotic convergence factor forn n interval matricesa with irreducible upper bound and nonnegative lower bound we compare the asymptotic convergence factor t of the total step method in interval analysis with the factor s of the corresponding single step method we derive a result similar to that of the theorem of stein and rosenberg furthermore we show that s can be less than the spectral radius of the real single step matrix corresponding to the total step matrix a where a is the absolute value ofa this answers an old question in interval analysis

parallel interval multisplittings we introduce interval multisplittings to enclose the sets a 1b a a b b where a denotes an interval matrix and b an interval vector the resulting iterative multisplitting methods have a natural parallelism we investigate these methods with respect to convergence speed of convergence and quality of the resulting enclosure fors

convergence of relaxed parallel multisplitting methods abstract multisplitting methods are parallel methods for the solution of a linear system ax b it has been observed that the convergence of multisplitting methods is often improved if some kind of relaxation is used we investigate two different variants of relaxed multisplitting methods if a is an h matrix these methods converge if the relaxation parameter is from an interval 0 0 with 0 1