Olshevsky V., Tyrtyshnikov E. Matrix Methods: Theory, Algorithms and Applications

Издательство World Scientific, 2010, -598 pp.This book is unique in covering the whole of a triptych consisting of algebraic theory, algorithmic problems, and numerical applications, all united by the essential use of matrix methods. This was the spirit of the 2nd International Conference on Matrix Methods and Operator Equations (23-27 July 2007, Moscow) hosted by the Institute of Numerical Mathematics of Russian Academy of Sciences and organized by Daria Bini, Gene Golub, Alexander Guterman, Vadim Olsbevsky, Stefano Serra-Capizzano, Gilbert Strang, and Eugene Tyrtyshnikov.
Matrix methods provide the key to many problems in pure and applied mathematics. However, it often happens that linear algebra theory, numerical algorithms, and matrices in FEM/BEM applications live as if in three separate worlds. In this book, perhaps for the first time at all, they are put together as one entity, all it was in the Moscow meeting, where the algebraic part was represented by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk.
Among the authors of this book are several top-class experts in numerical mathematics, matrix analysis, and linear algebra applications including Dario Bini, Walter Gander, Alexander Guterman, Wolfgang Hackbusch, Khakim Ikramov, Valery Il'in, Igor Kaporin, Boris Khoromskij, Victor Pan, Stefano Serra-Capizzano, Reinhold Schneider, Vladimir Sergeichuk, Harald Wimmer and others.
The book assumes a good knowledge of basic linear algebra and general mathematical background. Besides professionals, it is intended as well for a wider audience, in academia and industr y, of all those who consider using matrix methods in their work.
We are pleased to acknowledge that Alexander Guterman engaged in thorough editing "Algebra and Matrices" papers, Maxim Olshanskii and Yuri Vassilevski invested their time and expertise to the "Matrices and Applications" part, and Sergei Goreinov committed himself to producing a camera-ready manuscript. Support for the Moscow meeting which created the foundation for this book, by the Russian Foundation for Basic Research, the Russian Academy of Sciences, International Foundation for Technology and Investments, Neurok Techsoft, and the University of Insubria (Como, Italy). is gratefully acknowledged.Algebra and Matrices
Operators Preserving Primitivity for Matrix Pairs
Decompositions of Quaternions and Their Matrix Equivalents
Sensitivity Analysis of Hamiltonian and Reversible Systems Prone to Dissipation-Induced Instabilities
Block Triangular Miniversal Deformations of Matrices and Matrix Pencils
Determining the Schein Rank of Boolean Matrices
Lattices of Matrix Rows and Matrix Columns. Lattices of Invariant Column Eigenvectors
Matrix Algebras and Their Length
On a New Class of Singular Nonsymmetric Matrices with Nonnegative Integer Spectra
Reduction of a Set of Matrices over a Principal Ideal Domain to the Smith Normal Forms by Means of the Same One-Sided Transformations
Matrices and Algorithms
Nonsymmetric Algebraic Riccati Equations Associated with an M-Matrix: Recent Advances and Algorithms
A Generalized Conjugate Direction Method for Nonsymmetric Large Ill-Conditioned Linear Systems
There Exist Normal Hankel (φ,ψ)-Circulants of Any Order n
On the Treatment of Boundary Artifacts in Image Restoration by Reflection and/or Anti-Reflection
Zeros of Determinants of λ- Matrices
How to Find a Good Submatrix
Conjugate and Semi-Conjugate Direction Methods with Preconditioning Projectors
Some Relationships between Optimal Preconditioner and Superoptimal Preconditioner
Scaling, Preconditioning, and Superlinear Convergence in GMRES-Type Iterations
Toeplitz and Toeplitz-Block-Toeplitz Matrices and Their Correlation with Syzygies of Polynomials
Concepts of Data-Sparse Tensor-Product Approximation in Many-Particle Modelling
Separation of Variables in Nonlinear Fermi Equation
Faster Multipoint Polynomial Evaluation via Structured Matrices
Testing Pivoting Policies in Gaussian Elimination
Newton's Iteration for Matrix Inversion, Advances and Extensions
Truncated Decompositions and Filtering Methods with Reflective/Anti-Reflective Boundary Conditions: A Comparison
Discrete-Time Stability of a Class of Hermitian Polynomial Matrices with Positive Semidefinite Coefficients
Matrices and Applications
Splitting Algorithm for Solving Mixed Variational Inequalities with Inversely Strongly Monotone Operators
Multilevel Algorithm for Graph Partitioning
2D-Extension of Singular Spectrum Analysis: Algorithm and Elements of Theory
Application of Radon Transform for Fast Solution of Boundary Value Problems for Elliptic POE in Domains With Complicated Geometry
Application of a Multigrid Method to Solving Diffusion-Type Equations
Monotone Matrices and Finite Volume Schemes for Diffusion Problems Preserving Non-Negativity of Solution
Sparse Approximation of FEM Matrix for Sheet Current Integro-Differential Equation
The Method of Magnetic Field Computation in Presence of an Ideal Conductive Multiconnected Surface by using the Integro-Differential Equation of the First Kind
Spectral Model Order Reduction Preserving Passivity for Large Multipart RCLM Networks
New Smoothers in Multigrid Methods for Strongly Nonsymmetric Linear Systems
Operator Equations for Eddy Currents on Singular Carriers
Matrix Approach to Modelling of Polarized Radiation Transfer in Heterogeneous Systems
The Method of Regularization of Tikhonov Based on Augmented Systems