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Sprache: Deutsch
Verlag: Korntal, Hagen,, 2009
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In den WarenkorbPaperback. Zustand: New. Print on Demand. This book explores the effectiveness of Jacobi and QR methods in calculating eigenvalues and singular values. The author demonstrates that Jacobi methods yield higher accuracy than QR, and can attain optimal accuracy when componentwise relative uncertainties in the matrix entries are small. The book begins by introducing perturbation theory for eigenvalues and singular values, providing new insights into the sensitivity of these quantities to matrix perturbations. It then analyzes two-sided Jacobi for the symmetric positive definite eigenproblem, proving that it computes eigenvalues with near-optimal accuracy. The author also discusses one-sided Jacobi for the singular value decomposition, showing that it achieves similar accuracy. The book's significance lies in its rigorous mathematical analysis of Jacobi methods, providing a theoretical foundation for their effectiveness in practical computations. By clarifying the conditions under which Jacobi methods attain high accuracy, this book empowers researchers and practitioners to make informed choices when solving eigenvalue and singular value problems. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item.
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Taschenbuch. Zustand: Neu. Applied Mathematics and Scientific Computing | Zlatko Drmac (u. a.) | Taschenbuch | x | Englisch | 2010 | Springer US | EAN 9781441933904 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - Proceedings of the second conference on Applied Mathematics and Scientific Computing, held June 4-9, 2001 in Dubrovnik, Croatia.The main idea of the conference was to bring together applied mathematicians both from outside academia, as well as experts from other areas (engineering, applied sciences) whose work involves advanced mathematical techniques.During the meeting there were one complete mini-course, invited presentations, contributed talks and software presentations. A mini-course Schwarz Methods for Partial Differential Equations was given by Prof Marcus Sarkis (Worcester Polytechnic Institute, USA), and invited presentations were given by active researchers from the fields of numerical linear algebra, computational fluid dynamics , matrix theory and mathematical physics (fluid mechanics and elasticity). This volume contains the mini-course and review papers by invited speakers (Part I), as well as selected contributed presentations from the field of analysis, numerical mathematics, and engineering applications.
Sprache: Englisch
Verlag: Springer US, Springer New York, 2003
ISBN 10: 0306474263 ISBN 13: 9780306474262
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - Proceedings of the second conference on Applied Mathematics and Scientific Computing, held June 4-9, 2001 in Dubrovnik, Croatia.The main idea of the conference was to bring together applied mathematicians both from outside academia, as well as experts from other areas (engineering, applied sciences) whose work involves advanced mathematical techniques.During the meeting there were one complete mini-course, invited presentations, contributed talks and software presentations. A mini-course Schwarz Methods for Partial Differential Equations was given by Prof Marcus Sarkis (Worcester Polytechnic Institute, USA), and invited presentations were given by active researchers from the fields of numerical linear algebra, computational fluid dynamics , matrix theory and mathematical physics (fluid mechanics and elasticity). This volume contains the mini-course and review papers by invited speakers (Part I), as well as selected contributed presentations from the field of analysis, numerical mathematics, and engineering applications.
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