a note on the markov property of stochastic processes described by nonlinear fokker planck equations abstract we study the markov property of processes described by generalized fokker planck equations that are nonlinear with respect to probability densities such as mean field fokker planck equations and fokker planck equations related to generalized thermostatistics we show that their transient solutions describe non markov processes in contrast stationary solutions can describe markov processes as a result nonlinear fokker planck equations can be used to model transient non markov processes that converge to stationary markov processes

the monogenic signal this paper introduces a two dimensional 2 d generalization of the analytic signal this novel approach is based on the riesz transform which is used instead of the hilbert transform the combination of a 2 d signal with the riesz transformed one yields a sophisticated 2 d analytic signal the monogenic signal the approach is derived analytically from irrotational and solenoidal vector fields based on local amplitude and local phase an appropriate local signal representation that preserves the split of identity i e the invariance equivariance property of signal decomposition is presented this is one of the central properties of the one dimensional 1 d analytic signal that decomposes a signal into structural and energetic information we show that further properties of the analytic signal concerning symmetry energy allpass transfer function and orthogonality are also preserved and we compare this with the behavior of other approaches for a 2 d analytic signal as a central topic of this paper a geometric phase interpretation that is based on the relation between the 1 d analytic signal and the 2 d monogenic signal established by the radon 1986 transform is introduced possible applications of this relationship are sketched and references to other applications of the monogenic signal are given

on the bounds for the norms of cauchy toeplitz and cauchy hankel matrices in this paper we have established a lower and an upper bounds for the spectral norms of the general cauchy toeplitz matrices of the form t n 1 g i j h where g 1 k and h 1 moreover we have obtained an upper bounds for the spectral norm of the cauchy hankel matrices of the form h n 1 g i j h where g 1 k and h 1 in addition we have established a lower and an upper bounds for the euclidean norm of the hadamard product cauchy toeplitz and cauchy hankel matrices

on the spectral norms of cauchy toeplitz and cauchy hankel matrices in this study we have found upper and lower bounds for the spectral norm of cauchy toeplitz and cauchy hankel matrices in the forms t n 1 a i j b n i j 1 h n 1 a i j b n i j 1

matrices of sinc methods this paper gives a brief review of sinc methods with emphasis on the matrices of sinc methods a novel procedure is presented based on sinc convolution for solving a poisson problem over a rectangular region although some of the work of gragg may already be applied to the solution of sinc matrix problems this paper also points to new directions of matrix research

multiresolution monogenic signal analysis using the riesz laplace wavelet transform the monogenic signal is the natural 2d counterpart of the 1d analytic signal we propose to transpose the concept to the wavelet domain by considering a complexified version of the riesz transform which has the remarkable property of mapping a real valued primary wavelet basis of l2 r2 into a complex one the riesz operator is also steerable in the sense that it give access to the hilbert transform of the signal along any orientation having set those foundations we specify a primary polyharmonic spline wavelet basis of l2 r2 that involves a single mexican hat like mother wavelet laplacian of a b spline the important point is that our primary wavelets are quasi isotropic they behave like multiscale versions of the fractional laplace operator from which they are derived which ensures steerability we propose to pair these real valued basis functions with their complex riesz counterparts to specify a multiresolution monogenic signal analysis this yields a representation where each wavelet index is associated with a local orientation an amplitude and a phase we give a corresponding wavelet domain method for estimating the underlying instantaneous frequency we also provide a mechanism for improving the shift and rotation invariance of the wavelet decomposition and show how to implement the transform efficiently using perfect reconstruction filterbanks we illustrate the specific feature extraction capabilities of the representation and present novel examples of wavelet domain processing in particular a robust tensor based analysis of directional image patterns the demodulation of interferograms and the reconstruction of digital holograms

cauchy toeplitz matrices and some applications abstract some properties of cauchy toeplitz matrices of the form tn 1 i j 1 2 are investigated it is shown that minimal singular values of tn converge to zero with increasing n some applications of cauchy toeplitz matrices to the solution of singular integral equations by the method of discrete singularities are considered

singular values and eigenvalues of non hermitian block toeplitz matrices in this paper we are concerned with the analysis of the distribution and localization of the singular values of toeplitz matrices ftn f g generated by a p variate lebesgue integrable matrix valued function f q p c hk q we prove that the union of the essential ranges of the singular values of f is a proper weak cluster for the whole set of the singular values of ftn f g by showing that the number of outliers is strongly depending on the regularity features of the underlying function f in particular if f is continuous or from the krein algebra and p 1 then the cluster is proper other results concerning the extreme spectral behavior of ftn f g second order ergodic formulas and localization of eigenvalues of preconditioned matrices ft 1 n g tn f g are presented some examples of applications to the preconditioning of these results are also discussed c 1999 elsevier science b v all rights reserved msc 15a12 15a18 65f10

a note on singular values of cauchy toeplitz matrices abstract we consider the asymptotic behaviour of the smallest singular values of the n n sections of a general infinite cauchy toeplitz matrix

new transformations of cauchy matrices and trummer s problem abstract we show some new expressions for a cauchy matrix which enable us to simplify the solution of trummer s problem both in the general case and in the case where the input cauchy matrix is fixed for the problem whereas the input vector varies

new fast algorithms for polynomial interpolation and evaluation on the chebyshev node set abstract for a polynomial p x of a degree n we study its interpolation and evaluation on a set of chebyshev nodes x cos 2 1 2n 2 0 1 n this is easily reduced to applying discrete fourier transforms dfts to the auxiliary polynomial q n p x where 2 x 1 exp 1 2n we show the back and forth transition between p x and q based on the respective back and forth transformations of the variable 1 z 1 z y x 1 x 1 y z 2 all these transformations like the dfts are performed by using o n log n arithmetic operations which thus suffice in order to support both interpolation and evaluation of p x on the chebychev set as well as on some related sets of nodes this improves by factor log n the known arithmetic time bound for chebyshev interpolation and gives an alternative supporting algorithm for the record estimate of o n log n for chebyshev evaluation obtained by gerasoulis in 1987 and based on a distinct algorithm

a fast parallel bjorck pereyra type algorithm for solving cauchy linear equations abstract we propose a new fast o n 2 parallel algorithm for solving cauchy systems of linear equations we perform an a priori rounding error analysis and obtain componentwise bounds for the forward backward and residual errors these bounds indicate that for the class of totally positive cauchy matrices the new algorithm is forward and backward stable producing a remarkably high relative accuracy in particular hilbert linear systems often considered to be too ill conditioned to be attacked can be rapidly solved with high precision the results indicate a close resemblance between the numerical properties of cauchy matrices and the much studied vandermonde matrices in fact our proposed cauchy solver is an analog of the well known bjorck pereyra algorithm for vandermonde systems as a by product we obtain favorably backward error bounds for the original bjorck pereyra algorithm several computed examples illustrate a connection of high relative accuracy to the concepts of effective well conditioning and total positivity

a recurrence formula for the direct solution of singular integral equations abstract an iterative method for the solution of singular integral equations is given in this paper by developing a recurrence formula discretizing the above formula by using appropriate quadrature rules the solution of the singular integral equation is given in an extremely simple form the number of numerical operations required for such a solution is considerably reduced when compared to the number of operations required for a classical type of solution illustrative examples are given indicating the efficiency of the method it is shown that the number of operations in this procedure is only half the number of the operations for a typical numerical method the convergence of the method is studied in the space of holder continuous functions in the particular case of plane elasticity more efficient bounds are given in the same case it is proved that the procedure is equivalent to the schwarz s alternating method and convergence is assured 18

an efficient implementation of a conformal mapping method based on the szego kernel an implementation based on iterative techniques of a method to compute the riemann mapping function is presented the method has been recently introduced by n kerzman and the author it expresses the szego kernel as the solution of an integral equation of the second kind it is shown how to treat symmetric regions the algorithm is tested on five examples the numerical results show that the method is competitive with respect to accuracy stability and efficiency

likelihood ratio based biometric score fusion multibiometric systems fuse information from different sources to compensate for the limitations in performance of individual matchers we propose a framework for the optimal combination of match scores that is based on the likelihood ratio test the distributions of genuine and impostor match scores are modeled as finite gaussian mixture model the proposed fusion approach is general in its ability to handle 1 discrete values in biometric match score distributions 2 arbitrary scales and distributions of match scores 3 correlation between the scores of multiple matchers and 4 sample quality of multiple biometric sources experiments on three multibiometric databases indicate that the proposed fusion framework achieves consistently high performance compared to commonly used score fusion techniques based on score transformation and classification

complexity of computations with matrices and polynomials this paper reviews the complexity of polynomial and matrix computations as well as their various correlations to each other and some major techniques for the design of algebraic and numerical algorithms

on the distribution of the singular values of toeplitz matrices in 1920 g szego proved a basic result concerning the distribution of the eigenvalues n j of the toeplitz sections tn f where f l is a real valued function simple examples show that this result cannot hold in the case where f is not real valued in this note we give an extension of this theorem for the singular values of tn f when f f0 r0 with f0 real valued and r0 continuous periodic with period 2 and such that r0 1 in addition we apply the basic theorem of szego to resolve a question of c moler

fast gaussian elimination with partial pivoting for matrices with displacement structure fast o n 2 implementation of gaussian elimination with partial pivoting is designed for matrices possessing cauchy like displacement structure we show how toeplitz like toeplitz plus hankel like and vandermonde like matrices can be transformed into cauchy like matrices by using discrete fourier cosine or sine transform matrices in particular this allows us to propose a new fast o n 2 toeplitz solver gko which incorporates partial pivoting a large set of numerical examples showed that gko demonstrated stable numerical behavior and can be recommended for solving linear systems especially with nonsymmetric indefinite and ill conditioned positive definite toeplitz matrices it is also useful for block toeplitz and mosaic toeplitz toeplitz block matrices the algorithms proposed in this paper suggest an attractive alternative to look ahead approaches where one has to jump over ill conditioned leading submatrices which in the worst case requires o n 3 operations

classification on the monogenic scale space application to target recognition in sar image this paper introduces a novel classification strategy based on the monogenic scale space for target recognition in synthetic aperture radar sar image the proposed method exploits monogenic signal theory a multidimensional generalization of the analytic signal to capture the characteristics of sar image e g broad spectral information and simultaneous spatial localization the components derived from the monogenic signal at different scales are then applied into a recently developed framework sparse representation based classification src moreover to deal with the data set whose target classes are not linearly separable the classification via kernel combination is proposed where the multiple components of the monogenic signal are jointly considered into a unifying framework for target recognition the novelty of this paper comes from 1 the development of monogenic feature via uniformly downsampling normalization and concatenation of the components at various scales 2 the development of score level fusion for srcs and 3 the development of composite kernel learning for classification in particular the comparative experimental studies under nonliteral operating conditions e g structural modifications random noise corruption and variations in depression angle are performed the comparative experimental studies of various algorithms including the linear support vector machine and the kernel version the src and the variants kernel src kernel linear representation and sparse representation of monogenic signal are performed too the feasibility of the proposed method has been successfully verified using moving and stationary target acquiration and recognition database the experimental results demonstrate that significant improvement for recognition accuracy can be achieved by the proposed method in comparison with the baseline algorithms

a lagrange matrices approach to confluent cauchy matrices we present a new approach to study inversion and factorization properties of confluent cauchy matrices we consider a class of generalized vandermonde matrices called lagrange matrices that are connected in a simple way with the cauchy matrices we apply the methods introduced in adv appl math 10 1989 348 to obtain inversion and factorization theorems for lagrange matrices and their confluent forms and then derive corresponding results for cauchy matrices a lagrange matrix v is associated with a pair of vectors x0 x1 xn and y0 y1 yn v is the matrix representation of the substitution operator that sends the vector p x0 p x1 p xn t to the vector p y0 p y1 p yn t for any polynomial p of degree at most n

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

fast algorithms for multiple evaluations of the riemann zeta function the best previously know algorithm for evaluating the riemann zeta function it with bounded and t large to moderate accuracy was based on the rienmann siegel formula and required on the order of t 1 2 operations for each value that was computed new algorithms are presented in this paper which enable one to compute any single value of it with fixed and t t t t 1 2 in o te operations on numbers of o log t bits for any e 0 for example these algorithms lead to methods for numerically verifying the riemann hypothesis for the first n zeros in what is expected to be o n 1 e operations

a fast algorithm for the multiplication of generalized hilbert matrices with vectors on presente un algorithme rapide de complexite logarithmique pour la multiplication des matrices de hilbert generalisees par des vecteurs

factorizations of cauchy matrices the development of fast algorithms for the solution of linear systems of equations with a cauchy matrix has recently received considerable attention several of these algorithms factor a cauchy matrix or its inverse into triangular and possibly diagonal matrices the numerical properties of the factorization methods depend on the selection of pivots this note presents elementary derivations of some factorization methods and describes a new strategy for searching both rows and columns for suitable pivots

a unifying approach to some old and new theorems on distribution and clustering abstract a unifying approach is proposed to studying the distributions of eigenvalues and singular values of toeplitz matrices associated with a fourier series and multilevel toeplitz matrices associated with a multidimensional fourier series obtained are the extensions of the szego and avram parter theorems where the generating function is now required to belong to l 2 and not necessarily to l analogous extensions are given for multilevel toeplitz matrices in particular it is proved that if f x 1 x p l 2 then the p level complex toeplitz matrices allied with f have their singular values distributed as f x 1 x p the distribution results for the cesaro optimal circulants hold even if f l 1 also suggested are new theorems on clustering that have to do with the preconditioning of multilevel toeplitz matrices by multilevel circulants

lower bounds for the norms of cauchy toeplitz and cauchy hankel matrices in this study we have found lower bounds for the spectral norms and euclidean norms of cauchy toeplitz and cauchy hankel matrices in the forms t n 1 g i j h i j 1 n h n 1 g i j h i j 1 n

nystro m s iterative variant methods for the solution of cauchy singular integral equations iterative methods for the solution of algebraic systems and integral equations are becoming increasingly popular because they can take advantage of the speed of vector and parallel computers in this paper nystrom s iterative variant methods developed for the solution of fredholm integral equations are extended to the solution of cauchy singular integral equations gauss chebyshev and lobatto chebyshev quadrature approximations are used to define two iterative algorithms giv and liv and their convergence for all continuously differentiable kernels is proven for arbitrary kernels the complexity is o m 2 operations per iteration step where m is the number of node points however for certain kernels the complexity can be reduced to o m log 2 m by using a fast summation algorithm an extrapolation technique based on the average of the gauss chebyshev and lobatto chebyshev methods is also introduced the average is usually as accurate as the lobatto chebyshev or gauss chebyshev method with twice

quantitative statistical assessment of conditional models for synthetic aperture radar many applications of object recognition in the presence of pose uncertainty rely on statistical models conditioned on pose for observations the image statistics of three dimensional 3 d objects are often assumed to belong to a family of distributions with unknown model parameters that vary with one or more continuous valued pose parameters many methods for statistical model assessment for example the tests of kolmogorov smirnov and k pearson require that all model parameters be fully specified or that sample sizes be large assessing pose dependent models from a finite number of observations over a variety of poses can violate these requirements however a large number of small samples corresponding to unique combinations of object pose and pixel location are often available we develop methods for model testing which assume a large number of small samples and apply them to the comparison of three models for synthetic aperture radar images of 3 d objects with varying pose each model is directly related to the gaussian distribution and is assessed both in terms of goodness of fit and underlying model assumptions such as independence known mean and homoscedasticity test results are presented in terms of the functional relationship between a given significance level and the percentage of samples that wold fail a test at that level

classification via sparse representation of steerable wavelet frames on grassmann manifold application to target recognition in sar image automatic target recognition has been widely studied over the years yet it is still an open problem the main obstacle consists in extended operating conditions e g depression angle change configuration variation articulation and occlusion to deal with them this paper proposes a new classification strategy we develop a new representation model via the steerable wavelet frames the proposed representation model is entirely viewed as an element on grassmann manifolds to achieve target classification we embed grassmann manifolds into an implicit reproducing kernel hilbert space rkhs where the kernel sparse learning can be applied specifically the mappings of training sample in rkhs are concatenated to form an overcomplete dictionary it is then used to encode the counterpart of query as a linear combination of its atoms by designed grassmann kernel function it is capable to obtain the sparse representation from which the inference can be reached the novelty of this paper comes from 1 the development of representation model by the set of directional components of riesz transform 2 the quantitative measure of similarity for proposed representation model by grassmann metric and 3 the generation of global kernel function by grassmann kernel extensive comparative studies are performed to demonstrate the advantage of proposed strategy

myocardial motion estimation from medical images using the monogenic signal we present a method for the analysis of heart motion from medical images the algorithm exploits monogenic signal theory recently introduced as an n dimensional generalization of the analytic signal the displacement is computed locally by assuming the conservation of the monogenic phase over time a local affine displacement model is considered to account for typical heart motions as contraction expansion and shear a coarse to fine b spline scheme allows a robust and effective computation of the model s parameters and a pyramidal refinement scheme helps to handle large motions robustness against noise is increased by replacing the standard point wise computation of the monogenic orientation with a robust least squares orientation estimate given its general formulation the algorithm is well suited for images from different modalities in particular for those cases where time variant changes of local intensity invalidate the standard brightness constancy assumption this paper evaluates the method s feasibility on two emblematic cases cardiac tagged magnetic resonance and cardiac ultrasound in order to quantify the performance of the proposed method we made use of realistic synthetic sequences from both modalities for which the benchmark motion is known a comparison is presented with state of the art methods for cardiac motion analysis on the data considered these conventional approaches are outperformed by the proposed algorithm a recent global optical flow estimation algorithm based on the monogenic curvature tensor is also considered in the comparison with respect to the latter the proposed framework provides along with higher accuracy superior robustness to noise and a considerably shorter computation time

substitution permutation networks pseudorandom functions and natural proofs this article takes a new step towards closing the gap between pseudorandom functions prf and their popular bounded input length counterparts this gap is both quantitative because these counterparts are more efficient than prf in various ways and methodological because these counterparts usually fit in the substitution permutation network paradigm spn which has not been used to construct prf we give several candidate prf fi that are inspired by the spn paradigm most of our candidates are more efficient than previous ones our main candidates are as follows f1 0 1 n 0 1 n is an spn whose s box is a random function on b bits given as part of the seed we prove that f1 resists attacks that run in time 2eb f2 0 1 n 0 1 n is an spn where the s box is patched field inversion a common choice in practical constructions we show that f2 is computable with boolean circuits of size n logo 1 n and that it has exponential security 2 n against linear and differential cryptanalysis f3 0 1 n 0 1 is a nonstandard variant on the spn paradigm where states grow in length we show that f3 is computable with tc0 circuits of size n1 p e for any e 0 and that it is almost 3 wise independent f4 0 1 n 0 1 uses an extreme setting of the spn parameters one round one s box no diffusion matrix the s box is again patched field inversion we show that f4 is computable by circuits of size n logo 1 n and that it fools all parity tests on 20 9n outputs assuming the security of our candidates our work narrows the gap between the natural proofs barrier and existing lower bounds in three models circuits tc0 circuits and turing machines

approximate complex polynomial evaluation in near constant work per point given the n complex coefficients of a degree n 1 complex polynomial we wish to evaluate the polynomial at a large number m ge n of points on the complex plane this problem is required by many algebraic computations and so is considered in most basic algorithm texts e g a v aho j e hopcroft and j d ullman the design and analysis of computer algorithms addison wesley 1974 we assume an arithmetic model of computation where on each step we can execute an arithmetic operation which is computed exactly all previous exact algorithms c m fiduccia proceeding 4th annual acm symposium on theory of computing 1972 pp 88 93 h t kung fast evaluation and interpolation carnegie mellon 1973 a b borodin and i munro the computational complexity of algebraic and numerical problems american elsevier 1975 v pan a sadikou e landowne and o tiga comput math appl 25 1993 pp 25 30 cost at least work omega log 2 n per point and previously there were no known approximation algorithms for complex polynomial evaluation within the unit circle with work bounds better than the fastest known exact algorithms there are known approximation algorithms v rokhlin j complexity 4 1988 pp 12 32 v y pan j h reif and s r tate in proceedings 32nd annual ieee symposium on foundations of computer science 1992 pp 703 713 for polynomial evaluation at real points but these do not extend to evaluation at general points on the complex plane we provide approximation algorithms for complex polynomial evaluation that cost in many cases near constant amortized work per point let k log p epsilon where p is the sum of the moduli of the coefficients of the input polynomial p z let it tilde p z j be an epsilon approx of p z if epsilon upper bounds the modulus of the error of the approximation tilde p z j at each evaluation point zj that is p z j tilde p z j le epsilon note that epsilon is an absolute error bound rather than a relative error bound in many applications particularly in signal processing the evaluation points zj are fixed and require only polylogarithmic k log p epsilon o log o 1 n for these cases we get a surprising reduction in work by use of approximation algorithms as compared to the fastest known exact algorithms we epsilon approx complex degree n 1 polynomial evaluation at m ge n log n log 2 k fixed points on or within the unit disk in the complex plane in amortized work o log2 k per point which is o log2 log n for polylogarithmic k if the m points are not fixed then we have increased amortized work o log2 k log m per point which is o log m for polylogarithmic k and m ge n log n log k and is still substantially below the previous bound of omega log 2 m for known exact algorithms we further reduce our amortized bounds for special sets of evaluation points widely used in signal processing applications the chirp transform is equivalent to evaluating a complex degree n 1 polynomial at the chirp points which are zeta j j 0 dots m 1 for some fixed complex number zeta we epsilon approx complex degree n 1 polynomial evaluation at these m chirp points where m ge n log n log 2 k and zeta le 1 or ii m ge n and zeta le a function that limits to 1 for k o n and large n in amortized work o log k per point whereas the previous best bounds for exact evaluation via the chirp transform were omega log m per point a v aho k steiglitz and j d ullman siam j comput 4 1975 pp 533 539 using instead a reduction to approximate real polynomial evaluation by interpolation at the chebyshev points in total work o n log k we epsilon approx the evaluation of a degree n polynomial at the first n powers of the n th root of unity where n ge omega n 2 k and epsilon approx the n point dft for certain inputs with descending coefficient magnitude all of our results require polylogarithmic that is logo 1 n depth with the same work bounds we also provide a lower bound for a wide class of schemes for approximate evaluation of a degree n 1 polynomial on the unit circle namely we prove that if a scheme uses an approximation polynomial of degree k 1 then it can be convergent only over a small fraction o k n of the unit circle we believe this is the first lower bound of this sort proved and the proof uses an interesting reduction to the approximation of a matrix product by a matrix of reduced rank

singular values of cauchy toeplitz matrices abstract the behavior of singular values of matrices a n 1 i j g n i j 1 with n is investigated for any real g which is not integer it is proved that the singular values are clustered at sin g which is their upper boundary the only o n singular values are those which lie outside a given e neighborhood of the clustering point o n n 0 as n o n o ln 2 n holds if g 1 2 also proved is that the minimum singular values of a n g tend to zero provided that g 1 2

superfast algorithms for cauchy like matrix computations and extensions abstract an effective algorithm of m morf ph d thesis department of electrical engineering stanford university stanford ca 1974 in proceedings of the ieee international conference on assp ieee computer society press silver spring md 1980 pp 954 959 r r bitmead and b d o anderson linear algebra appl 34 1980 103 116 computes the solution x t 1 b to a strongly nonsingular toeplitz or toeplitz like linear system t x b a short displacement generator for the inverse t 1 of t and det t we extend this algorithm to the similar computations with n n cauchy and cauchy like matrices recursive triangular factorization of such a matrix can be computed by our algorithm at the cost of executing o nr 2 log 3 n arithmetic operations where r is the scaling rank of the input cauchy like matrix c r 1 if c is a cauchy matrix consequently the same cost bound applies to the computation of the determinant of c a short scaling generator of c 1 and the solution to a nonsingular linear system of n equations with such a matrix c our algorithm does not use the reduction to toeplitz like computations we also relax the assumptions of strong nonsingularity and even nonsingularity of the input not only for the computations in the field of complex or real numbers but even where the algorithm runs in an arbitrary field we achieve this by using randomization and we also show a certain improvement of the respective algorithm by kaltofen for toeplitz like computations in an arbitrary field our subject has close correlation to rational tangential matrix interpolation under passivity condition e g to nevanlinna pick tangential interpolation problems and has further impact on the decoding of algebraic codes

memory index of first passage time a simple measure of non markovian character on developpe la theorie pour le second moment de la variable de premier temps de passage des flots statistiques a memoire et on l applique a un mouvement brownien libre non markovien

fast triangular factorization of the sum of quasi toeplitz and quasi hankel matrices abstract the literature contains several recent fast algorithms for the triangular factorization of strongly regular toeplitz plus hankel matrices in this paper we study the rather more general sum of quasi toeplitz and quasi hankel matrices both hermitian and non hermitian quasi toeplitz and quasi hankel matrices are those that are congruent to toeplitz and hankel matrices in a special sense the derivation is based on the concept of displacement structure and its intimate relation to the schur reduction procedure for triangular factorization various special cases covering displacement ranks from two to eight are considered several other problems e g factorization of the inverse matrix solution of exact or overdetermined linear systems can be reduced to the direct factorization problem

complexity of multiplication with vectors for structured matrices abstract fast algorithms for computing the product with a vector are presented for a number of classes of matrices whose properties relate to the properties of toeplitz vandermonde or cauchy matrices these matrices are defined using the concept of displacement of a matrix and also for their inverses all the actions which are not dependent upon the coordinates of the input vector are singled out in a separate preprocessing stage the proposed algorithms are based on new representations of these matrices involving factor circulants

effects of time delay in stationary properties of a logistic growth model with correlated noises abstract a time delayed tumor cell growth model with correlated noises is investigated in the condition of small delay time the stationary probability distribution is derived and the stationary mean value x s t and normalized variance 2 of the tumor cell population and state transition rate between two steady states are numerically calculated the results indicate that i the delay time enhances the coherence resonance in x s t as a function of the multiplicative noise intensity d and increases x s t as a function of the additive noise intensity i e enhances fluctuation of the system however the strength of correlations between multiplicative and additive noise plays a contrary role to on these ii enhances the coherence resonance in as a function of d and increases as a function of i e speeds up the rate of state transition however also plays a contrary role to on these

displacement structure theory and applications in this survey paper we describe how strands of work that are important in two different fields matrix theory and complex function theory have come together in some work on fast computational algorithms for matrices with what we call displacement structure in particular a fast triangularization procedure can be developed for such matrices generalizing in a striking way an algorithm presented by schur 1917 j reine angew math 147 1917 pp 205 232 in a paper on checking when a power series is bounded in the unit disc this factorization algorithm has a surprisingly wide range of significant applications going far beyond numerical linear algebra we mention among others inverse scattering analytic and unconstrained rational interpolation theory digital filter design adaptive filtering and state space least squares estimation

on the lower bounds for the norms of cauchy toeplitz and cauchy hankel matrices abstract in this paper we give lower bounds for the euclidean norms and spectral norms of cauchy toeplitz matrices and cauchy hankel matrices in the forms t n 1 g i j h i j 1 n h n 1 g i j h i j 1 n respectively

some results on complex toeplitz eigenvalues we consider the asymptotics of the eigenvalues of toeplitz matrices generated by a complex valued symbol f which is essentially bounded we prove that if the essential range of f has empty interior and does not separate the complex plane then the corresponding toeplitz eigenvalues have the canonical distribution in the sense of widom the assumptions on the symbol only concern the topological structure of its essential range and are completely independent of its smoothness properties we also prove some clustering properties of eigenvalues and some new distribution results

pivoting and backward stability of fast algorithms for solving cauchy linear equations abstract three fast o n2 algorithms for solving cauchy linear systems of equations are proposed a rounding error analysis indicates that the backward stability of these new cauchy solvers is similar to that of gaussian elimination thus suggesting to employ various pivoting techniques to achieve a favorable backward stability it is shown that cauchy structure allows one to achieve in o n2 operations partial pivoting ordering of the rows and several other judicious orderings in advance without actually performing the elimination the analysis also shows that for the important class of totally positive cauchy matrices it is advantageous to avoid pivoting which yields a remarkable backward stability of the suggested algorithms it is shown that vandermonde and chebyshev vandermonde matrices can be efficiently transformed into cauchy matrices using discrete fourier cosine or sine transforms this allows us to use the proposed algorithms for cauchy matrices for rapid and accurate solution of vandermonde and chebyshev vandermonde linear systems the analytical results are illustrated by computed examples

relaxation and phase space singularities in time series of human magnetoencephalograms as indicator of photosensitive epilepsy to analyze the crucial role of fluctuation and relaxation effects for the function of the human brain we studied some statistical quantifiers that support the information characteristics of neuromagnetic brain responses magnetoencephalogram meg the signals to a flickering stimulus of different color combinations have been obtained from a group of control subjects which is then contrasted with those of a patient suffering photosensitive epilepsy pse we found that the existence of the specific stratification of the phase clouds and the concomitant relaxation singularities of the corresponding nonequilibrium dynamics of the chaotic behavior of the signals in separate areas in a patient provide likely indicators for the zones which are responsible for the appearance of pse

the prolate matrix abstract the purpose of this note is to describe some properties of a particular positive definite toeplitz matrix of arbitrary order which we call the prolate matrix this matrix arises naturally in signal processing and it is extremely ill conditioned moreover its eigenvalues exhibit rather unusual behavior making it a very useful test matrix for computational algorithms