on the reconstruction of toeplitz matrix inverses from columns abstract in this paper we discuss the problem whether and how the inverse of a toeplitz matrix can be recovered from some of its columns or parts of columns under the requirement that only 2 n 1 parameters are involved the results generalize and strengthen earlier findings by trench gohberg semencul krupnik ben artzi shalom labahn rodman and others special attention is paid to symmetric skewsymmetric and hermitian toeplitz matrix inverses and the question whether such a matrix can be retrieved from a single column

a korovkin type theory for finite toeplitz operators via matrix algebras preconditioned conjugate gradients pcg are widely and successfully used methods for solving a toeplitz linear system a n vec x vec b 59 9 20 5 34 62 6 10 28 45 44 46 49 frobenius optimal preconditioners are chosen in some proper matrix algebras and are defined by minimizing the frobenius distance from a n the convergence features of these pcg have been naturally studied by means of the weierstrass jackson theorem 17 36 45 owing to the profound relationship between the spectral features of the matrices a n generated by the fourier coefficients of a continuous function f and the analytical properties of the symbol f itself in this paper we capsize this point of view by showing that the optimal preconditioners can be used to define both new and just known linear positive operators uniformly approximating the function f on the other hand by modifying the korovkin theorem to study the frobenius optimal preconditioning problem we provide a new and unifying tool for analyzing all frobenius optimal preconditioners in any generic matrix algebra related to trigonometric transforms finally the multilevel case is sketched and discussed by showing that a korovkin type theory also holds in a multivariate sense

inversion of toeplitz matrices with only two standard equations abstract it is shown that the invertibility of a toeplitz matrix can be determined through the solvability of two standard equations the inverse matrix is represented by two of its columns which are the solutions of the two standard equations and the entries of the original toeplitz matrix

conformal invariance in two dimensional percolation the word percolation borrowed from the latin refers to the seeping or oozing of a liquid through a porous medium usually to be strained in this and related senses it has been in use since the seventeenth century it was introduced more recently into mathematics by s r broadbent and j m hammersley bh and is a branch of probability theory that is especially close to statistical mechanics broadbent and hammersley distinguish between two types of spreading of a fluid through a medium or between two aspects of the probabilistic models of such processes diffusion processes in which the random mechanism is ascribed to the fluid and percolation processes in which it is ascribed to the medium a percolation process typically depends on one or more probabilistic parameters for example if molecules of a gas are absorbed at the surface of a porous solid as in a gas mask then their ability to penetrate the solid depends on the sizes of the pores in it and their positions both conceived to be distributed in some random manner a simple mathematical model of such a process is often defined by taking the pores to be distributed in some regular manner that could be determined by a periodic graph and to be open thus very large or closed thus smaller than the molecules with probabilities p and 1 p as p increases the probability of deeper penetration of the gas into the interior of the solid grows

analytical inversion of symmetric tridiagonal matrices in this paper we present an analytical formula for the inversion of symmetrical tridiagonal matrices the result is of relevance to the solution of a variety of problems in mathematics and physics as an example the formula is used to derive an exact analytical solution for the one dimensional discrete poisson equation with dirichlet boundary conditions

kernelized multiview projection for robust action recognition conventional action recognition algorithms adopt a single type of feature or a simple concatenation of multiple features in this paper we propose to better fuse and embed different feature representations for action recognition using a novel spectral coding algorithm called kernelized multiview projection kmp computing the kernel matrices from different features views via time sequential distance learning kmp can encode different features with different weights to achieve a low dimensional and semantically meaningful subspace where the distribution of each view is sufficiently smooth and discriminative more crucially kmp is linear for the reproducing kernel hilbert space which allows it to be competent for various practical applications we demonstrate kmp s performance for action recognition on five popular action datasets and the results are consistently superior to state of the art techniques

markov chain sampling of the o n loop models on the infinite plane a numerical method was recently proposed in herdeiro and doyon phys rev e 94 043322 2016 10 1103 physreve 94 043322 showing a precise sampling of the infinite plane two dimensional critical ising model for finite lattice subsections the present note extends the method to a larger class of models namely the o n loop gas models for n 1 2 we argue that even though the gibbs measure is nonlocal it is factorizable on finite subsections when sufficient information on the loops touching the boundaries is stored our results attempt to show that provided an efficient markov chain mixing algorithm and an improved discrete lattice dilation procedure the planar limit of the o n models can be numerically studied with efficiency similar to the ising case this confirms that scale invariance is the only requirement for the present numerical method to work

factorized banded inverse preconditioners for matrices with toeplitz structure in this paper we study factorized banded inverse preconditioners for matrices with toeplitz structure we show that if a toeplitz matrix t has certain off diagonal decay property then the factorized banded inverse preconditioner approximates t 1 accurately and the spectra of these preconditioned matrices are clustered around 1 in nonlinear image restoration applications toeplitz related systems of the form i t d t are required to solve where d is a positive nonconstant diagonal matrix we construct inverse preconditioners for such matrices numerical results show that the performance of our proposed preconditioners are superior to that of circulant preconditioners a two dimensional nonlinear image restoration example is also presented to demonstrate the effectiveness of the proposed preconditioner

critical behaviour of the two dimensional potts model with a continuous number of states a finite size scaling analysis we investigate the critical behaviour of the two dimensional q state potts model using finite size scaling and transfer matrix methods for the continuous transition range 0 these results for continuous q were obtained from a transfer matrix constructed for a generalized whitney polynomial representing the potts models an effective algorithm to compute the dominant eigenvalues of this essentially nonsymmetric transfer matrix is developed

diagonally striped matrices and approximate inverse preconditioners the inverse of a banded matrix is in general dense if the structure of the original banded matrix is striped that is the non zero diagonals are separated by one or more zero diagonals the inverse may exhibit a similar striped structure the motivation for studying inverses of striped matrices is to obtain efficient preconditioners for systems arising from radiation transport equations whose matrices include dominant values along diagonal stripes linear systems whose system matrix has a striped inverse lend themselves to the use of a sparse approximate inverse spai preconditioner whose structure is derived from that of the actual inverse

recursive based pcg methods for toeplitz systems with nonnegative generating functions in this paper we consider the solutions of symmetric positive definite but ill conditioned toeplitz systems an x b here we propose to solve the system by the recursive based preconditioned conjugate gradient method the idea is to use the inverse of am the principal submatrix of an with the gohberg semencul formula as a preconditioner for an the inverse of am can be generated recursively by using the formula until m is small enough the construction of the preconditioners requires only the entries of an and does not require the explicit knowledge of the generating function f of an we show that if f is a nonnegative bounded and piecewise continuous even function with a finite number of zeros of even order the spectra of the preconditioned matrices are uniformly bounded except for a fixed number of outliers hence the conjugate gradient method when applied to solving the preconditioned system converges very quickly numerical results are included to illustrate the effectiveness of our approach

the elements of finite order in the riordan group over the complex field abstract an element of finite order in the riordan group over the real field must have order 1 or 2 if we extend all the entries to be complex numbers then it may have any finite order in the present paper we investigate the elements of finite order of the riordan group over the complex field this notion leads us to define an element of pseudo order k 2 and k pseudo involution respectively it turns out that the inverse of a k pseudo involution only differs from it in signs we clarify some relationship between the elements of pseudo order k and k pseudo involutions in particular k pseudo involutions for k 0 mod 4 are characterized by a single sequence the subgroups of the riordan group formed by the elements having pseudo order of a prime power p r are also introduced

on the extreme eigenvalues of hermitian block toeplitz matrices abstract we are concerned with the behavior of the minimum maximum eigenvalue 0 n n n of an n 1 n 1 hermitian toeplitz matrix tn where is an integrable real valued function kac murdoch and szego widom parter and r h chan obtained that 0 n min o 1 n2k in the case where c2k at least locally and inf has a zero of order 2k we obtain the same result under the second hypothesis alone moreover we develop a new tool in order to estimate the extreme eigenvalues of the mentioned matrices proving that the rate of convergence of 0 n to inf depends only on the order not necessarily even or integer or finite of the zero of inf with the help of this tool we derive an absolute lower bound for the minimal eigenvalues of toeplitz matrices generated by nonnegative l1 functions and also an upper bound for the associated euclidean condition numbers finally these results are extended to the case of hermitian block toeplitz matrices with toeplitz blocks generated by a bivariate integrable function

image set based face recognition using self regularized non negative coding and adaptive distance metric learning simple nearest neighbor classification fails to exploit the additional information in image sets we propose self regularized nonnegative coding to define between set distance for robust face recognition set distance is measured between the nearest set points samples that can be approximated from their orthogonal basis vectors as well as from the set samples under the respective constraints of self regularization and nonnegativity self regularization constrains the orthogonal basis vectors to be similar to the approximated nearest point the nonnegativity constraint ensures that each nearest point is approximated from a positive linear combination of the set samples both constraints are formulated as a single convex optimization problem and the accelerated proximal gradient method with linear time euclidean projection is adapted to efficiently find the optimal nearest points between two image sets using the nearest points between a query set and all the gallery sets as well as the active samples used to approximate them we learn a more discriminative mahalanobis distance for robust face recognition the proposed algorithm works independently of the chosen features and has been tested on gray pixel values and local binary patterns experiments on three standard data sets show that the proposed method consistently outperforms existing state of the art methods

a priori sparsity patterns for parallel sparse approximate inverse preconditioners parallel algorithms for computing sparse approximations to the inverse of a sparse matrix either use a prescribed sparsity pattern for the approximate inverse or attempt to generate a good pattern as part of the algorithm this paper demonstrates that for pde problems the patterns of powers of sparsified matrices psms can be used a priori as effective approximate inverse patterns and that the additional effort of adaptive sparsity pattern calculations may not be required psm patterns are related to various other approximate inverse sparsity patterns through matrix graph theory and heuristics concerning the pde s green s function a parallel implementation shows that psm patterned approximate inverses are significantly faster to construct than approximate inverses constructed adaptively while often giving preconditioners of comparable quality

parallel and superfast algorithms for hankel systems of equations utilizing kernel structure properties a unified construction of hankel matrix inversion algorithms is presented three types of algorithms are obtained 1 o n 2 complexity levinson type 2 o n parallel complexity schur type and 3 o n log2 n complexity asymptotically fast ones all algorithms work without additional assumption like strong nonsingularity

skew cyclic displacements and inversions of two innovative patterned matrices in this paper we deal mainly with a class of column upper plus lower cupl toeplitz matrices without toeplitz structure which are close to the toeplitz matrices in the sense that their 1 1 cyclic displacements coincide with cyclic displacement of some toeplitz matrices by constructing the corresponding displacement of the matrices we derive the formulas on representation of the inverses of the cupl toeplitz matrices in the form of sums of products of factor 1 1 circulants and 1 1 circulants furthermore through the relation between the cupl toeplitz matrices and the cupl hankel matrices the inverses of the cupl hankel matrices can be obtained as well

lazy random walks for superpixel segmentation we present a novel image superpixel segmentation approach using the proposed lazy random walk lrw algorithm in this paper our method begins with initializing the seed positions and runs the lrw algorithm on the input image to obtain the probabilities of each pixel then the boundaries of initial superpixels are obtained according to the probabilities and the commute time the initial superpixels are iteratively optimized by the new energy function which is defined on the commute time and the texture measurement our lrw algorithm with self loops has the merits of segmenting the weak boundaries and complicated texture regions very well by the new global probability maps and the commute time strategy the performance of superpixel is improved by relocating the center positions of superpixels and dividing the large superpixels into small ones with the proposed optimization algorithm the experimental results have demonstrated that our method achieves better performance than previous superpixel approaches

the inverses of block hankel and block toeplitz matrices a set of new formulae for the inverse of a block hankel or block toeplitz matrix is given the formulae are expressed in terms of certain matrix pade forms which approximate a matrix power series associated with the block hankel matrix by using frobenius type identities between certain matrix pade forms the inversion formulae are shown to generalize the formulae of gohberg heinig and in the scalar case the formulae of gohberg semencul and gohberg krupnik the new formulae have the significant advantage of requiring only that the block hankel matrix itself be nonsingular the other formulae require in addition that certain submatrices be nonsingular since effective algorithms for computing the required matrix pade forms are available the formulae are practical indeed some of the algorithms allow for the efficient calculation of the inverse not only of the given block hankel matrix but also of any nonsingular block principal minor

the best circulant preconditioners for hermitian toeplitz systems in this paper we propose a new family of circulant preconditioners for ill conditioned hermitian toeplitz systems a x b the preconditioners are constructed by convolving the generating function f of a with the generalized jackson kernels for an n by n toeplitz matrix a the construction of the preconditioners requires only the entries of a and does not require the explicit knowledge of f when f is a nonnegative continuous function with a zero of order 2p the condition number of a is known to grow as o n2p we show however that our preconditioner is positive definite and the spectrum of the preconditioned matrix is uniformly bounded except for at most 2p 1 outliers moreover the smallest eigenvalue is uniformly bounded away from zero hence the conjugate gradient method when applied to solving the preconditioned system converges linearly the total complexity of solving the system is therefore of o n log n operations in the case when f is positive we show that the convergence is superlinear numerical results are included to illustrate the effectiveness of our new circulant preconditioners

a sparse approximate inverse preconditioner for the conjugate gradient method a method for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix a is developed and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient calculations it is proved that in exact arithmetic the preconditioner is well defined if a is an h matrix the results of numerical experiments are presented

face recognition using sparse approximated nearest points between image sets we propose an efficient and robust solution for image set classification a joint representation of an image set is proposed which includes the image samples of the set and their affine hull model the model accounts for unseen appearances in the form of affine combinations of sample images to calculate the between set distance we introduce the sparse approximated nearest point sanp sanps are the nearest points of two image sets such that each point can be sparsely approximated by the image samples of its respective set this novel sparse formulation enforces sparsity on the sample coefficients and jointly optimizes the nearest points as well as their sparse approximations unlike standard sparse coding the data to be sparsely approximated are not fixed a convex formulation is proposed to find the optimal sanps between two sets and the accelerated proximal gradient method is adapted to efficiently solve this optimization we also derive the kernel extension of the sanp and propose an algorithm for dynamically tuning the rbf kernel parameter while matching each pair of image sets comprehensive experiments on the ucsd honda cmu mobo and youtube celebrities face datasets show that our method consistently outperforms the state of the art

approximate inverse free preconditioners for toeplitz matrices abstract in this paper we propose approximate inverse free preconditioners for solving toeplitz systems the preconditioners are constructed based on the famous gohberg semencul formula we show that if a toeplitz matrix is generated by a positive bounded function and its entries enjoys the off diagonal decay property then the eigenvalues of the preconditioned matrix are clustered around one experimental results show that the proposed preconditioners are superior to other existing preconditioners in the literature

critical exponents of two dimensional potts and bond percolation models critical exponents of the two dimensional q state potts model are calculated by means of finite size scaling and transfer matrix techniques for continuous q results for the temperature exponent agree accurately with the conjecture of den nijs 1979 the magnetic exponent is found to behave in accordance with the conjecture of nienhuis et al 1980

image clustering using local discriminant models and global integration in this paper we propose a new image clustering algorithm referred to as clustering using local discriminant models and global integration ldmgi to deal with the data points sampled from a nonlinear manifold for each data point we construct a local clique comprising this data point and its neighboring data points inspired by the fisher criterion we use a local discriminant model for each local clique to evaluate the clustering performance of samples within the local clique to obtain the clustering result we further propose a unified objective function to globally integrate the local models of all the local cliques with the unified objective function spectral relaxation and spectral rotation are used to obtain the binary cluster indicator matrix for all the samples we show that ldmgi shares a similar objective function with the spectral clustering sc algorithms e g normalized cut ncut in contrast to ncut in which the laplacian matrix is directly calculated based upon a gaussian function a new laplacian matrix is learnt in ldmgi by exploiting both manifold structure and local discriminant information we also prove that k means and discriminative k means diskmeans are both special cases of ldmgi extensive experiments on several benchmark image datasets demonstrate the effectiveness of ldmgi we observe in the experiments that ldmgi is more robust to algorithmic parameter when compared with ncut thus ldmgi is more appealing for the real image clustering applications in which the ground truth is generally not available for tuning algorithmic parameters

learning to hash with optimized anchor embedding for scalable retrieval sparse representation and image hashing are powerful tools for data representation and image retrieval respectively the combinations of these two tools for scalable image retrieval i e sparse hashing sh methods have been proposed in recent years and the preliminary results are promising the core of those methods is a scheme that can efficiently embed the high dimensional image features into a low dimensional hamming space while preserving the similarity between features existing sh methods mostly focus on finding better sparse representations of images in the hash space we argue that the anchor set utilized in sparse representation is also crucial which was unfortunately underestimated by the prior art to this end we propose a novel sh method that optimizes the integration of the anchors such that the features can be better embedded and binarized termed as sparse hashing with optimized anchor embedding the central idea is to push the anchors far from the axis while preserving their relative positions so as to generate similar hashcodes for neighboring features we formulate this idea as an orthogonality constrained maximization problem and an efficient and novel optimization framework is systematically exploited extensive experiments on five benchmark image data sets demonstrate that our method outperforms several state of the art related methods

determination of stripe structures for finite element matrics stripe structures were introduced by the author parallel computing to appear as a means for the inclusion of the nonzero elements of a sparse matrix into a regular pattern which allows for efficient parallel manipulation in this paper the stripe structures of stiffness matrices resulting from irregular domains covered by regular grids are analyzed it is proved that the nonzero elements in these matrices may be covered by very few stripes and that these stripes may be nonoverlapping if the nodes of the grids are numbered appropriately the exact number of stripes which is independent of the size of the problem is derived for different types of grids and different numbering schemes the stripe structures of some irregular grids are also examined

local feature discriminant projection in this paper we propose a novel subspace learning algorithm called local feature discriminant projection lfdp for supervised dimensionality reduction of local features lfdp is able to efficiently seek a subspace to improve the discriminability of local features for classification we make three novel contributions first the proposed lfdp is a general supervised subspace learning algorithm which provides an efficient way for dimensionality reduction of large scale local feature descriptors second we introduce the differential scatter discriminant criterion dsdc to the subspace learning of local feature descriptors which avoids the matrix singularity problem third we propose a generalized orthogonalization method to impose on projections leading to a more compact and less redundant subspace extensive experimental validation on three benchmark datasets including uiuc sports scene 15 and mit indoor demonstrates that the proposed lfdp outperforms other dimensionality reduction methods and achieves state of the art performance for image classification

statistical computations on grassmann and stiefel manifolds for image and video based recognition in this paper we examine image and video based recognition applications where the underlying models have a special structure the linear subspace structure we discuss how commonly used parametric models for videos and image sets can be described using the unified framework of grassmann and stiefel manifolds we first show that the parameters of linear dynamic models are finite dimensional linear subspaces of appropriate dimensions unordered image sets as samples from a finite dimensional linear subspace naturally fall under this framework we show that an inference over subspaces can be naturally cast as an inference problem on the grassmann manifold to perform recognition using subspace based models we need tools from the riemannian geometry of the grassmann manifold this involves a study of the geometric properties of the space appropriate definitions of riemannian metrics and definition of geodesics further we derive statistical modeling of inter and intraclass variations that respect the geometry of the space we apply techniques such as intrinsic and extrinsic statistics to enable maximum likelihood classification we also provide algorithms for unsupervised clustering derived from the geometry of the manifold finally we demonstrate the improved performance of these methods in a wide variety of vision applications such as activity recognition video based face recognition object recognition from image sets and activity based video clustering

on inversion of toeplitz matrices in 1992 labahn and shalom showed that the inverse of a toeplitz matrix can be reconstructed by two of its columns and by some entries of the original toeplitz matrix we here present a modification of this result and another shorter proof

on algebras of toeplitz matrices abstract necessary and sufficient conditions for toeplitz and block toeplitz matrices to have toeplitz inverse are given maximal algebras of scalar toeplitz matrices are fully described

remarks on the inversion of hankel matrices the paper continues the investigation into the links between algebraic system theory more specifically the partial realization problem and the problem of hankel matrix inversion the representation of the inverse of a hankel matrix as a bezoutiant and the bezout equation play a principal role

distance metric learning for large margin nearest neighbor classification the accuracy of k nearest neighbor knn classification depends significantly on the metric used to compute distances between different examples in this paper we show how to learn a mahalanobis distance metric for knn classification from labeled examples the mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes knn classification using euclidean distances in our approach the metric is trained with the goal that the k nearest neighbors always belong to the same class while examples from different classes are separated by a large margin as in support vector machines svms the margin criterion leads to a convex optimization based on the hinge loss unlike learning in svms however our approach requires no modification or extension for problems in multiway as opposed to binary classification in our framework the mahalanobis distance metric is obtained as the solution to a semidefinite program on several data sets of varying size and difficulty we find that metrics trained in this way lead to significant improvements in knn classification sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster we show how to learn and combine these local metrics in a globally integrated manner

optimal quasi optimal and superlinear band toeplitz preconditioners for asymptotically ill conditioned positive definite toeplitz systems in this paper we are concerned with the solution of n x n hermitian toeplitz systems with nonnegative generating functions f the preconditioned conjugate gradient pcg method with the well known circulant preconditioners fails in the case where f has zeros in this paper we consider as preconditioners band toeplitz matrices generated by trigonometric polynomials g of fixed degree l we use different strategies of approximation of f to devise a polynomial g which has some analytical properties of f is easily computable and is such that the corresponding preconditioned system has a condition number bounded by a constant independent of n for each strategy we analyze the cost per iteration and the number of iterations required for the convergence within a preassigned accuracy we obtain different estimates of l for which the total cost of the proposed pcg methods is optimal and the related rates of convergence are superlinear finally for the most economical strategy we perform various numerical experiments which fully confirm the effectiveness of approximation theory tools in the solution of this kind of linear algebra problems

a sparse approximate inverse preconditioner for nonsymmetric linear systems this paper is concerned with a new approach to preconditioning for large sparse linear systems a procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient type methods some theoretical properties of the preconditioner are discussed and numerical experiments on test matrices from the harwell boeing collection and from tim davis s collection are presented our results indicate that the new preconditioner is cheaper to construct than other approximate inverse preconditioners furthermore the new technique insures convergence rates of the preconditioned iteration which are comparable with those obtained with standard implicit preconditioners

improved schur complement preconditioners for block toeplitz systems with small size blocks in this paper we employ the preconditioned conjugate gradient method with the improved schur complement preconditioners for hermitian positive definite block toeplitz systems with small size blocks schur complement preconditioners have been proved to be an effective method for such block toeplitz systems ching et al 2007 the modification is based on taylor expansion approximation we prove that the matrices preconditioned by improved schur preconditioners have more clustered spectra compared to that of the schur complement preconditioners hence preconditioned conjugate gradient type methods will converge faster numerical examples are given to demonstrate the efficiency of the proposed method

inversion of toeplitz structured matrices using only standard equations formulas for the inverse of layered or striped toeplitz matrices in terms of solutions of standard equations are given these results are also generalized in the generic case to mosaic toeplitz matrices and also to toeplitz plus hankel matrices

on inversion of toeplitz and close to toeplitz matrices abstract it is proved that three columns of an inverse of a scalar toeplitz matrix when properly chosen are always enough to reconstruct it a parametrization of invertible toeplitz matrices in terms of the first and a combination of two consecutive columns of the inverse matrix is also given

a numerical experimental study of inverse preconditioning for the parallel iterative solution to 3d finite element flow equations integration of the subsurface flow equation by finite elements fe in space and finite differences fd in time requires the repeated solution to sparse symmetric positive definite systems of linear equations iterative techniques based on preconditioned conjugate gradients pcg are one of the most attractive tool to solve the problem on sequential computers a present challenge is to make pcg attractive in a parallel computing environment as well to this aim a key factor is the development of an efficient parallel preconditioner fsai factorized sparse approximate inverse and enlarged fsai relying on the approximate inverse of the coefficient matrix appears to be a most promising parallel preconditioner in the present paper pcg using fsai diagonal and parms parallel algebraic recursive multilevel solvers preconditioners is implemented on the ibm sp4 512 and clx 768 supercomputers with up to 32 processors to solve underground flow problems of a large size the results show that fsai may allow for a parallel relative efficiency e p larger than 50 on the largest problems with p 32 processors moreover fsai turns out to be significantly less expensive and more robust than parms finally it is shown that e p for p in the upper range may be much improved if pcg fsai is implemented on clx

inverse problems for hankel and toeplitz matrices abstract the problem is considered how to construct a toeplitz or hankel matrix a from one or two equations of the form au g the general solution is described explicitly special cases are inverse spectral problems for hankel and toeplitz matrices and problems from the theory of orthogonal polynomials

correlation functions of twist operators applied to single self avoiding loops the o n spin model in two dimensions may equivalently be formulated as a loop model and then mapped to a height model which is conjectured to flow under the renormalization group to a conformal field theory cft at the critical point the order n terms in the partition function and correlation functions describe single self avoiding loops we investigate the ensemble of these self avoiding loops using twist operators which count loops which wind non trivially around them with a factor 1 these turn out to have level 2 null states and hence their correlators satisfy a set of partial differential equations we show that partly connected parts of the four point function count the expected number of loops which separate one pair of points from the other pair and find an explicit expression for this we argue that the differential equation satisfied by these expectation values should have an interpretation in terms of a stochastic schramm loewner evolution sle process with 6 the two point function in a simply connected domain satisfies a closely related set of equations we solve these and hence calculate the expected number of single loops which separate both points from the boundary

duplex metric learning for image set classification image set classification has attracted much attention because of its broad applications despite the success made so far the problems of intra class diversity and inter class similarity still remain two major challenges to explore a possible solution to these challenges this paper proposes a novel approach termed duplex metric learning dml for image set classification the proposed dml consists of two progressive metric learning stages with different objectives used for feature learning and image classification respectively the metric learning regularization is not only used to learn powerful feature representations but also well explored to train an effective classifier at the first stage we first train a discriminative stacked autoencoder dsae by layer wisely imposing a metric learning regularization term on the neurons in the hidden layers and meanwhile minimizing the reconstruction error to obtain new feature mappings in which similar samples are mapped closely to each other and dissimilar samples are mapped farther apart at the second stage we discriminatively train a classifier and simultaneously fine tune the dsae by optimizing a new objective function which consists of a classification error term and a metric learning regularization term finally two simple voting strategies are devised for image set classification based on the learnt classifier in the experiments we extensively evaluate the proposed framework for the tasks of face recognition object recognition and face verification on several commonly used data sets and state of the art results are achieved in comparison with existing methods

an approximate inverse preconditioner for toeplitz systems with multiple right hand sides abstract we are interested in preconditioning techniques for symmetric positive definite but ill conditioned toeplitz systems with multiple right hand sides tx b here the right hand sides are available simultaneously our main idea is to use an approximate inverse of t as a preconditioner for t the approximate inverse of t is generated by the inverse formula given by lv and huang x g lv t z huang a note on inversion of toeplitz matrices appl math lett 20 2007 1189 1193 the construction of the preconditioner is of low computational cost requires only the entries of t and does not require explicit knowledge of the generating function f of t we show that if given a proper parameter then the approximate inverse preconditioner approximates t 1 accurately and thus the spectra of these preconditioned matrices are clustered around 1 it follows that the conjugate gradient method converges very quickly when applied to solve the preconditioned systems numerical results are given to demonstrate the effectiveness of our preconditioner

cyclic displacements and decompositions of inverse matrices for cupl toeplitz matrices abstract in this paper we deal mainly with a class of cupl toeplitz matrices 32 without toeplitz structure which are close to the toeplitz matrices in the sense that their 1 1 cyclic displacements coincide with cyclic displacement of some toeplitz matrices by constructing the corresponding displacement of the matrices we derive the formulas on representation of the inverses of the cupl toeplitz matrices in the form of sums of products of factor row first plus last right circulants furthermore the inverses of the cupl hankel matrices can be also obtained which benefits from the relation between the cupl toeplitz matrices and the cupl hankel matrices

on bezoutians of nonsquare matrix polynomials and inversion of matrices with nonsquare blocks abstract the notion of bezoutian of nonsquare matrix polynomials is defined it is used to establish formulae for the inverse of square matrices partitioned into nonsquare blocks in particular a generalization of the gohberg semencul formula for the inverse of a generalized toeplitz matrix is proved

parallel preconditioning with sparse approximate inverses a parallel preconditioner is presented for the solution of general sparse linear systems of equations a sparse approximate inverse is computed explicitly and then applied as a preconditioner to an iterative method the computation of the preconditioner is inherently parallel and its application only requires a matrix vector product the sparsity pattern of the approximate inverse is not imposed a priori but captured automatically this keeps the amount of work and the number of nonzero entries in the preconditioner to a minimum rigorous bounds on the clustering of the eigenvalues and the singular values are derived for the preconditioned system and the proximity of the approximate to the true inverse is estimated an extensive set of test problems from scientific and industrial applications provides convincing evidence of the effectiveness of this approach

monte carlo method to calculate the central charge and critical exponents a typical problem with monte carlo simulations in statistical physics is that they do not allow for a direct calculation of the free energy for systems at criticality this means that one cannot calculate the central charge in a monte carlo simulation we present a novel finite size scaling technique for two dimensional systems on a geometry of lxm and focus on the scaling behavior in m l we show that the finite size scaling behavior of the stress tensor the operator that governs the anisotropy of the system allows for a determination of the central charge and critical exponents the expectation value of the stress tensor can be calculated using monte carlo simulations unexpectedly it turns out that the stress tensor is remarkably insensitive for critical slowing down rendering it an easy quantity to simulate we test the method for the ising model with central charge c 1 2 the ashkin teller model c 1 and the f model also c 1

monte carlo method for critical systems in infinite volume the planar ising model in this paper we propose a monte carlo method for generating finite domain marginals of critical distributions of statistical models in infinite volume the algorithm corrects the problem of the long range effects of boundaries associated to generating critical distributions on finite lattices it uses the advantage of scale invariance combined with ideas of the renormalization group in order to construct a type of holographic boundary condition that encodes the presence of an infinite volume beyond it we check the quality of the distribution obtained in the case of the planar ising model by comparing various observables with their infinite plane prediction we accurately reproduce planar two three and four point of spin and energy operators we also define a lattice stress energy tensor and numerically obtain the associated conformal ward identities and the ising central charge

global least squares method gl lsqr for solving general linear systems with several right hand sides abstract in this paper we propose a new method for solving general linear systems with several right hand sides this method is based on global least squares method and reduces the original matrix to the lower bidiagonal form we derive a simple recurrence formula for generating the sequence of approximate solutions x k some theoretical properties of the new method are discussed and we also show that how this method can be implemented for the sylvester equation finally some numerical experiments on test matrices are presented to show the efficiency of the new method