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. Key Features ? Represents possibly the first-ever compilation in one volume of a triptych of algebraic theory, algorithmic problems and numerical applications ? Consists of a selection of papers on the most contemporary research lines in mathematics with essential use of matrix methods ? The contributors are several top-class experts in numerical mathematics, matrix analysis and linear algebra applications: 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, amongst others ? An important figure in numerical analysis, Gene Golub, delivered his ?Golub?s dimension? in probably one of his last appearances before passing on shortly after

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