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Intersecting two large research areas--numerical analysis and applied probability/quering theory--this book is a self -contained introduction to the numerical solution of structured Markov chains, which have a wide applicability in queueing theory and stochastic modeling. Aimed at graduates and researchers in numerical analysis, applied mathematics, probability, engineering and computer science it provides a thorough overview of the current literature. The book, consisting of nine chapters, is presented in three parts. Part 1 covers a basic description of the fundamental concepts related to Markov chains, a systematic treatment of the structure matrix tools, including finite Toeplitz matrices, displacement operators, FFT, and the infinite block Toeplitz matrices, their relationship with matrix power series and the fundamental problems of solving matrix equations can computing canonical factorizations. Part 2 deals with the description and analysis of structure Markov chains and includes M/G/1, quasi-birth0death processes, non-skip-free queries and tree-like processes. Part 3 covers solution algorithms where new convergence and applicability results are proved. Each chapter ends with bibliographic notes for further reading, and the book ends with an appendix collecting the main general concepts and results used in the book, a list of the main annotations and algorithms used in the book, and an extensive index.

Numerical analysis --- Stochastic processes --- Markov processes --- Markov, Processus de --- Numerical solutions. --- Solutions numériques --- Solutions numériques

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This book presents a collection of expository and research papers on various topics in matrix and operator theory, contributed by several experts on the occasion of Albrecht Böttcher’s 60th birthday. Albrecht Böttcher himself has made substantial contributions to the subject in the past. The book also includes a biographical essay, a complete bibliography of Albrecht Böttcher’s work and brief informal notes on personal encounters with him. The book is of interest to graduate and advanced undergraduate students majoring in mathematics, researchers in matrix and operator theory as well as engineers and applied mathematicians.

Mathematics. --- Matrix theory. --- Algebra. --- Operator theory. --- Linear and Multilinear Algebras, Matrix Theory. --- Operator Theory. --- Toeplitz operators. --- Toeplitz matrices. --- Böttcher, Albrecht. --- Operators, Toeplitz --- Böttcher, A. --- Matrices --- Linear operators --- Functional analysis --- Mathematics --- Mathematical analysis

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This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to the topics where Georg Heinig had made outstanding achievements. In particular, this includes contributions from the fields of structured matrices, fast algorithms, operator theory, and applications to system theory and signal processing.

Matrices. --- Operator theory. --- Signal processing --Mathematics. --- System theory. --- Operator theory --- Matrices --- System theory --- Signal processing --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Algebra --- Calculus --- Applied Mathematics --- Mathematics. --- Systems, Theory of --- Systems science --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Functional analysis. --- Numerical analysis. --- Numerical Analysis. --- Operator Theory. --- Functional Analysis. --- Functional analysis --- Science --- Algebra, Abstract --- Algebra, Universal --- Philosophy --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematical analysis

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This book gathers selected contributions presented at the INdAM Meeting Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, held in Cortona, Italy on September 4-8, 2017. Highlights cutting-edge research on Structured Matrix Analysis, it covers theoretical issues, computational aspects, and applications alike. The contributions, written by authors from the foremost international groups in the community, trace the main research lines and treat the main problems of current interest in this field. The book offers a valuable resource for all scholars who are interested in this topic, including researchers, PhD students and post-docs.

Algebras, Linear --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Numerical analysis. --- Matrix theory. --- Numerical Analysis. --- Linear and Multilinear Algebras, Matrix Theory. --- Algebra. --- Mathematics