Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
620
result(s) for
"Moment problems (Mathematics)"
Sort by:
Matrices, Moments and Quadrature with Applications
This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part.
Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization.
This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.
eBook
Moments and moment invariants in pattern recognition
Moments as projections of an image's intensity onto a proper polynomial basis can be applied to many different aspects of image processing.These include invariant pattern recognition, image normalization, image registration, focus/ defocus measurement, and watermarking.
eBook
2D and 3D Image Analysis by Moments
Presents recent significant and rapid development in the field of 2D and 3D image analysis 2D and 3D Image Analysis by Moments, is a unique compendium of moment-based image analysis which includes traditional methods and also reflects the latest development of the field.
eBook
Weighted shifts on directed trees
A new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated.
Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and of weighted adjacency
operators, on the other; they are called weighted shifts on directed trees. The basic properties of such operators, including
closedness, adjoints, polar decomposition and moduli are studied. Circularity and the Fredholmness of weighted shifts on directed trees
are discussed. The relationships between domains of a weighted shift on a directed tree and its adjoint are described. Hyponormality,
cohyponormality, subnormality and complete hyperexpansivity of such operators are entirely characterized in terms of their weights.
Related questions that arose during the study of the topic are solved as well. Particular trees with one branching vertex are
intensively studied mostly in the context of subnormality and complete hyperexpansivity of weighted shifts on them. A strict connection
of the latter with
eBook
Hamburger moment completions and its applications
Moment problems arise naturally in many areas of Mathematics, Economics and Operations research. While moment problems have numerous applications to extremal problems, optimization and limit theorems in probability theory, they rely on a complete set of moments or truncated moment sequences. Due to missing moment entries or availability of truncated moment sequences, sometimes we need to work in the space of incomplete moment sequences. Moment problems with missing entries are closely related to Hankel matrix completion problems. In this dissertation we give solutions to Hamburger moment problems with missing entries. The problem of completing partial positive sequences is considered. The main result is a characterization of positive (semi)definite completable patterns, namely patterns that guarantee the existence of a Hamburger moment completion of a partial positive (semi)definite sequence. Moreover, several patterns which are not positive definite completable are given. Furthermore, we characterize the determinate case by certain subsequence of given moment sequence. For a positive sequence if its subsequence with the pattern of arithmetic progression is determinate, then the sequence is determinate. Also, if a sequence is indeterminate then its subsequences with pattern of arithmetic progression are indeterminate. In the last part of this thesis, we apply moment completion problems to reconstruct Radon transform with missing data. Radon transform is a well known tool for reconstructing data from its projections. Reconstruction of Radon transform with missing data is closely related to reconstruction of a function from moment sequences with missing terms. A new range theorem is established for the Radon transform based on the Hamburger moment problem in two variables, and the sparse moment problem is converted into the Radon transform with missing data and vice versa. A modified Radon transform is introduced and its inversion formula is established.
Dissertation
Flat extensions of positive moment matrices : recursively generated relations
In this book, the authors develop new computational tests for existence and uniqueness of representing measures $\\mu$ in the Truncated Complex Moment Problem: $\\gamma_{ij}=\\int \\bar z^iz^j\\, d\\mu$ $(0\\1e i+j\\1e 2n)$. Conditions for the existence of finitely atomic representing measures are expressed in terms of positivity and extension properties of the moment matrix $M(n)(\\gamma)$ associated with $\\gamma \\equiv \\gamma ^{(2n)}$: $\\gamma_(00), \\dots, \\gamma_{0,2n},\\dots, \\gamma _{2n,0}$, $\\gamma_{00}>0$.This study includes new conditions for flat (i.e., rank-preserving) extensions $M(n+1)$ of $M(n)\\ge 0$; each such extension corresponds to a distinct rank $M(n)$-atomic representing measure, and each such measure is minimal among representing measures in terms of the cardinality of its support. For a natural class of moment matrices satisfying the tests of recursive generation, recursive consistency, and normal consistency, the existence problem for minimal representing measures is reduced to the solubility of small systems of multivariable algebraic equations.In a variety of applications, including cases of the quartic moment problem ($n=2$), the text includes explicit contructions of minimal representing measures via the theory of flat extensions. Additional computational texts are used to prove non-existence of representing measures or the non-existence of minimal representing measures. These tests are used to illustrate, in very concrete terms, new phenomena, associated with higher-dimensional moment problems that do not appear in the classical one-dimensional moment problem.
eBook
On boundary interpolation for matrix valued Schur functions
A number of interpolation problems are considered in the Schur class of $p\\times q$ matrix valued functions $S$ that are analytic and contractive in the open unit disk. The interpolation constraints are specified in terms of nontangential limits and angular derivatives at one or more (of a finite number of) boundary points. Necessary and sufficient conditions for existence of solutions to these problems and a description of all the solutions when these conditions are met is given. The analysis makes extensive use of a class of reproducing kernel Hilbert spaces ${\\mathcal{H}}(S)$ that was introduced by de Branges and Rovnyak. The Stein equation that is associated with the interpolation problems under consideration is analyzed in detail. A lossless inverse scattering problem is also considered.
eBook