perturbation bound of the drazin inverse a perturbation theory for the drazin inverse a d is developed this theory is based on the jordan canonical form of a norm estimates of a e a d are derived when a d and a e are of the same rank and e is small a hard problem by campbell and meyer linear algebra appl 10 1975 77 83 is partially solved

classified vector quantization of images vector quantization vq provides many attractive features for image coding with high compression ratios however initial studies of image coding with vq have revealed several difficulties most notably edge degradation and high computational complexity we address these two problems and propose a new coding method classified vector quantization cvq which is based on a composite source model blocks with distinct perceptual features such as edges are generated from different subsources i e belong to different classes in cvq a classifier determines the class for each block and the block is then coded with a vector quantizer designed specifically for that class we obtain better perceptual quality with significantly lower complexity with cvq when compared to ordinary vq we demonstrate with cvq visual quality which is comparable to that produced by existing coders of similar complexity for rates in the range 0 6 1 0 bits pixel

perturbation of the drazin inverse for matrices with equal eigenprojections at zero abstract let a denote the eigenprojection of a matrix a corresponding to the eigenvalue 0 we characterize matrices b such that b a and derive from the results 1 error bounds for the drazin inverse of a perturbation 2 improvement of error bounds given recently by wei 10 wei and wang 11 and castro gonzalez et al 4 and 3 a new characterization of ep matrices

on the inverse mean first passage matrix problem and the inverse m matrix problem abstract the inverse mean first passage time problem is given a positive matrix m r n n then when does there exist an n state discrete time homogeneous ergodic markov chain c whose mean first passage matrix is m the inverse m matrix problem is given a nonnegative matrix a then when is a an inverse of an m matrix the main thrust of this paper is to show that the existence of a solution to one of the problems can be characterized by the existence of a solution to the other in so doing we extend earlier results of tetali and fiedler

image compression with variable block size segmentation high quality variable rate image compression is achieved by segmenting an image into regions of different sizes classifying each region into one of several perceptually distinct categories and using a distinct coding procedure for each category segmentation is performed with a quadtree data structure by isolating the perceptually more important areas of the image into small regions and separately identifying larger random texture blocks since the important regions have been isolated the remaining parts of the image can be coded at a lower rate than would be otherwise possible high quality coding results are achieved at rates between 0 35 and 0 7 b p depending on the nature of the original image and satisfactory results have been obtained at 0 25 b p

a smooth variational principle with applications to subdifferentiability and to differentiability of convex functions we show that typically lower semicontinuous functions on a banach space densely inherit lower subderivatives of the same degree of smoothness as the norm in particular every continuous convex function on a space with a g teaux weak hadamard frechet smooth renorm is densely g teaux weak hadamard frechet differentiable our technique relies on a more powerful analogue of ekeland s variational principle in which the function is perturbed by a quadratic like function this smooth variational principle has very broad applicability in problems of nonsmooth analysis

characterizations of inverse m matrices with special zero patterns in this paper we provide some characterizations of inverse m matrices with special zero patterns in particular we give necessary and sufficient conditions for k diagonal matrices and symmetric k diagonal matrices to be inverse m matrices in addition results for triadic matrices tridiagonal matrices and symmetric 5 diagonal matrices are presented as corollaries

perturbation bounds for the generalized inverses at s 2 with application to constrained linear system in this paper the more general perturbation problem of the generalized inverse a t s 2 is considered we derive its perturbation bounds when the subspaces t and s also have perturbation and in special case when t and s have no perturbation we get some results on the condition numbers with respect to a t s 2 and constrained linear system ax b x t which are similar to the regular inverse a 1 and nonsingular linear system ax b

continuity properties of the 1 inverse and perturbation bounds for the drazin inverse there are known results about the continuity of the important pseudoinverses we extend some well known results to the 1 inverse as for the drazin inverse which is not a 1 inverse we present new perturbation bounds

error bounds for a general perturbation of the drazin inverse the paper solves a long standing problem of finding error bounds for a general perturbation of the drazin inverse the bounds are given in terms of the distance between the matrices together with the distance between their eigenprojections estimates using the gap between subspaces are also given recent results of several authors including castro koliha straskraba soochov j math to appear wang and wei linear algebra appl 258 1997 179 186 can be recovered as special cases of our theorems

on the structure of vector quantizers vector quantization is intrinsically superior to predictive coding transform coding and other suboptimal and em ad hoc procedures since it achieves optimal rate distortion performance subject only to a constraint on memory or block length of the observable signal segment being encoded the key limitation of existing techniques is the very large randomly generated code books which must be stored and the computational complexity of the associated encoding procedures the quantization operation is decomposed into its rudimentary structural components this leads to a simple and elegant approach to derive analytical properties of optimal quantizers some useful properties of quantizers and algorithmic approaches are given which are relevant to the complexity of both storage and processing in the encoding operation highly disordered quantizers which have been designed using a clustering algorithm are considered finally lattice quantizers are examined which circumvent the need for a code book by using a highly structured code based on lattices the code vectors are algorithmically generated in a simple manner rather than stored in a code book and fast algorithms perform the encoding algorithm with negligible complexity

a lossless image compression algorithm using variable block size segmentation the redundancy in digital image representation can be classified into two categories local and global in this paper we present an analysis of two image characteristics that give rise to local and global redundancy in image representation based on this study we propose a lossless image compression scheme that exploits redundancy both at local and global levels in order to obtain maximum compression efficiency the proposed algorithm segments the image into variable size blocks and encodes them depending on the characteristics exhibited by the pixels within the block the proposed algorithm is implemented in software and its performance is better than other lossless compression schemes such as the huffman the arithmetic the lempel ziv and the jpeg

acute perturbation of the group inverse abstract for any n n complex matrix a let a g be the group inverse of a when a is singular a matrix b a e is said to be an acute perturbation of a if e is small and the spectral radius b g b a g a 1 the acute perturbation coincides with the stable perturbation of the group inverse if the matrix b satisfies condition r b n a 0 n b r a 0 which was introduced by castro gonzalez et al 2008 8 furthermore several examples are provided to illustrate the acute perturbation of the group inverse

error bounds for the perturbation of the drazin inverse under some geometrical conditions this paper studies the drazin inverse for perturbed matrices for that given a square matrix a we consider and characterize the class of matrices b with index s such that r ba d n a d 0 n a db r a d 0 and r b s r ba d where n a and r a denote the null space and the range space of a matrix a respectively and a d denote the drazin inverse of a then we provide explicit representations for b d and bb d and upper bounds for the relative error b d a email protected a email protected and the error bb d aa email protected a numerical example illustrates that the obtained bounds are better than others given in the literature

the drop theorem the petal theorem and ekeland s variational principle on montre que le principe variationnel d ekeland ou plus precisement une forme legerement modifiee est une consequence d un resultat geometrique connu sous le terme de theoreme de la goutte

lossless image compression and encryption using scan abstract this paper presents a new methodology which performs both lossless compression and encryption of binary and gray scale images the compression and encryption schemes are based on scan patterns generated by the scan methodology the scan is a formal language based two dimensional spatial accessing methodology which can efficiently specify and generate a wide range of scanning paths or space filling curves this paper presents a brief overview of scan compression and decompression algorithms encryption and decryption algorithms and test results of the methodology

the error bound of the perturbation of the drazin inverse abstract let a and e be n n matrices and b a e denote the drazin inverse of a by a d in this paper we give an upper bound for the relative error b d a d a d 2 and a lower bound for b d 2 under certain circumstances the continuity properties and the derivative of the drazin inverse are also considered

image coding using vector quantization a review a review of vector quantization techniques used for encoding digital images is presented first the concept of vector quantization is introduced then its application to digital images is explained spatial predictive transform hybrid binary and subband vector quantizers are reviewed the emphasis is on the usefulness of the vector quantization when it is combined with conventional image coding techniques or when it is used in different domains

an expression of the drazin inverse of a perturbed matrix given a square matrix a and its perturbation matrix e a new expression for the drazin inverse b d of b a e is derived if aa db 2 aa db 2 or b 2aa d baa d 2 based on the new expression a bound of the relative error of b d is developed some known results in the literature on the drazin inverse and the perturbation bound are included by this new formula as special cases a numerical example is given to compare the upper bounds

a note on the perturbation bound of the drazin inverse a perturbation bound for the drazin inverse a d with ind a e 1 has recently been developed however those upper bounds are not satisfied since it is not tight enough in this paper a sharper upper bounds for a e a d with weaker conditions is derived that new bound is also a generalization of a new general upper bound of the group inverse we also derive a new expression of the drazin inverse a e d with ind a e 1 and the corresponding upper bound of a e d a d in a special case numerical examples are given to illustrate the sharpness of the new bounds

the strong ekeland variational principle the strong drop theorem and applications on donne une nouvelle demonstration du theoreme de la goutte generalisee en utilisant des formes renforcees du principe variationnel d ekeland et du theoreme de la goutte et donne de nouveaux resultats et de nouvelles demonstrations de resultats connus sur les proprietes generiques des problemes de minimisation convexes et non convexes