Compared to other books devoted to matrices, this volume is unique in covering the whole of a triptych consisting of algebraic theory, algorithmic problems and numerical applications, all united by the essential use and urge for development of matrix methods. This was the spirit of the 2nd International Conference on Matrix Methods and Operator Equations from 23–27 July 2007 in Moscow that was organized by Dario Bini, Gene Golub, Alexander Guterman, Vadim Olshevsky, Stefano Serra-Capizzano, Gilbert Strang and Eugene Tyrtyshnikov.Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume.The soul of the meeting was Gene Golub, who rendered a charming “Golub's dimension” to the three main axes of the conference topics. This volume is dedicated in gratitude to his memory.Contents:Algebra and Matrices:Operators Preserving Primitivity for Matrix Pairs (L B Beasley & A E Guterman)Determining the Schein Rank of Boolean Matrices (E E Marenich)Matrix Algebras and Their Length (O V Markova)Matrices and Algorithms:Some Relationships Between Optimal Preconditioner and Superoptimal Preconditioner (J-B Chen et al.)Separation of Variables in Nonlinear Fermi Equation (Yu I Kuznetsov)Faster Multipoint Polynomial Evaluation via Structured Matrices (B Murphy & R E Rosholt)Matrices and Applications:Multilevel Algorithm for Graph Partitioning (N S Bochkarev et al.)Operator Equations for Eddy Currents on Singular Carriers (J Naumenko)Matrix Approach to Modelling of Polarized Radiation Transfer in Heterogeneous Systems (T A Sushkevich et al.)and other papersReadership: Advanced graduate students in mathematics and professionals. Besides the academia and industry, also those who consider using matrix methods in their work or who major in other fields of mathematics, engineering and sciences.
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