*This book is a revised version of the first edition, regarded as a classic in its field.*

**Author**: Richard S. Varga

**Publisher:** Springer Science & Business Media

**ISBN:** 9783642051548

**Category:** Mathematics

**Page:** 358

**View:** 588

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This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorporated in the revision, and in other places, new material has been added to the chapters in the form of additional up-to-date references and some recent theorems to give readers some new directions to pursue.
This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorporated in the revision, and in other places, new material has been added to the chapters in the form of additional up-to-date references and some recent theorems to give readers some new directions to pursue.
This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorporated in the revision, and in other places, new material has been added to the chapters in the form of additional up-to-date references and some recent theorems to give readers some new directions to pursue.
This comprehensive book is presented in two parts; the first part introduces the basics of matrix analysis necessary for matrix computations, and the second part presents representative methods and the corresponding theories in matrix computations. Among the key features of the book are the extensive exercises at the end of each chapter. Matrix Analysis and Computations provides readers with the matrix theory necessary for matrix computations, especially for direct and iterative methods for solving systems of linear equations. It includes systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods, as well as current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. This book can be used as a textbook for graduate students as well as a self-study tool and reference for researchers and engineers interested in matrix analysis and matrix computations. It is appropriate for courses in numerical analysis, numerical optimization, data science, and approximation theory, among other topics
This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.
A valuable resource book for students, tutors and researchers using iterative methods.
This treatment starts with basics and progresses to sweepout process for obtaining complete solution of any given system of linear equations and role of matrix algebra in presentation of useful geometric ideas, techniques, and terminology.
This book treats state-of-the-art computational methods for power flow studies and contingency analysis. In the first part the authors present the relevant computational methods and mathematical concepts. In the second part, power flow and contingency analysis are treated. Furthermore, traditional methods to solve such problems are compared to modern solvers, developed using the knowledge of the first part of the book. Finally, these solvers are analyzed both theoretically and experimentally, clearly showing the benefits of the modern approach.
This volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions--that is, the factorization of matrices into products of similar ones. The first two chapters provide the required background from mathematics and computer science needed to work effectively in matrix computations. The remaining chapters are devoted to the LU and QR decompositions--their computation and applications. The singular value decomposition is also treated, although algorithms for its computation will appear in the second volume of the series. The present volume contains 65 algorithms formally presented in pseudocode. Other volumes in the series will treat eigensystems, iterative methods, sparse matrices, and structured problems. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. To give the series focus, the emphasis is on algorithms, their derivation, and their analysis. The reader is assumed to have a knowledge of elementary analysis and linear algebra and a reasonable amount of programming experience, typically that of the beginning graduate engineer or the undergraduate in an honors program. Strictly speaking, the individual volumes are not textbooks, although they are intended to teach, the guiding principle being that if something is worth explaining, it is worth explaining fully. This has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study.
This classic textbook provides a modern and complete guide to the calculation of eigenvalues of matrices, written at an accessible level that presents in matrix notation the fundamental aspects of the spectral theory of linear operators in finite dimension. Unique features of Eigenvalues of matrices, revised edition are the convergence of eigensolvers serving as the basis of the notion of the gap between invariant subspaces, its coverage of the impact of the high nonnormality of the matrix on its eigenvalues, and the comprehensive nature of the material that moves beyond mathematical technicalities to the essential mean carried out by matrix eigenvalues.
Iterative Methods for Linear Systems÷offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.÷÷
This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.
This volume is intended to mark the 75th birthday of A R Mitchell, of the University of Dundee. It consists of a collection of articles written by numerical analysts having links with Ron Mitchell, as colleagues, collaborators, former students, or as visitors to Dundee. Ron Mitchell is known for his books and articles contributing to the numerical analysis of partial differential equations; he has also made major contributions to the development of numerical analysis in the UK and abroad, and his many human qualitites are such that he is held in high regard and looked on with great affection by the numerical analysis community. The list of contributors is evidence of the esteem in which he is held, and of the way in which his influence has spread through his former students and fellow workers. In addition to contributions relevant to his own specialist subjects, there are also papers on a wide range of subjects in numerical analysis.

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*This book is a revised version of the first edition, regarded as a classic in its field.*

**Author**: Richard S. Varga

**Publisher:** Springer Science & Business Media

**ISBN:** 9783642051548

**Category:** Mathematics

**Page:** 358

**View:** 588

*This book is a revised version of the first edition, regarded as a classic in its field.*

**Author**: Richard S. Varga

**Publisher:** Springer

**ISBN:** 3642051618

**Category:** Mathematics

**Page:** 358

**View:** 470

**Author**: Richard S. Varga

**Publisher:**

**ISBN:** OCLC:631065339

**Category:** Differential equations, Partial

**Page:** 322

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*This book is a revised version of the first edition, regarded as a classic in its field.*

**Author**: Richard S. Varga

**Publisher:** Springer

**ISBN:** 3540663215

**Category:** Mathematics

**Page:** 358

**View:** 725

**Author**: Centre International de Rencontres Mathématiques

**Publisher:**

**ISBN:** OCLC:248053086

**Category:**

**Page:** 279

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**Author**: Zbigniew Ignacy Woźnicki

**Publisher:**

**ISBN:** OCLC:1202624349

**Category:**

**Page:** 470

**View:** 793

*325) [329] R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1962. The Second Edition, Springer-Verlag, Berlin, 2000. (Cited on pp. 134, 141, 142, 156, 162, 191, 196, 199, 224, 225, 233, 242, 406) [330] R. S. ...*

**Author**: Zhong-Zhi Bai

**Publisher:** SIAM

**ISBN:** 9781611976632

**Category:** Mathematics

**Page:** 496

**View:** 664

*This self-contained monograph presents matrix algorithms and their analysis.*

**Author**: Wolfgang Hackbusch

**Publisher:** Springer

**ISBN:** 9783662473245

**Category:** Mathematics

**Page:** 511

**View:** 263

*R.S. Varga , " Matrix Iterative Analysis " , Prentice - Hall , Englewood Cliffs , N.J. , 1962 . 6. D.M. Young , " Iterative solution of large linear systems " , Academic Press , New York , 1971 . 7. P. Concus and G.H.Golub , " Use of ...*

**Author**:

**Publisher:**

**ISBN:** OSU:32435026678797

**Category:** Computers

**Page:**

**View:** 851

*On approximate inverses of block H - matrices , in Numerical Analysis and Mathematical Modelling . ... An iterative solution method for linear systems of which the coefficient matrix is a symmetric M - matrix . Math . Comp .*

**Author**: Owe Axelsson

**Publisher:** Cambridge University Press

**ISBN:** 0521555698

**Category:** Mathematics

**Page:** 672

**View:** 599

*The Theory of Matrices, 2nd ed. New York: Chelsea, 1946. ... matrix. inequalities. M. Marcus and H. Mine. A Survey of Matrix Theory and Matrix Inequalities. Boston: Allyn and Bacon, 1964. ... Matrix Iterative Analysis.*

**Author**: Franz E. Hohn

**Publisher:** Courier Corporation

**ISBN:** 9780486143729

**Category:** Mathematics

**Page:** 544

**View:** 532

*To stop the iteration process, some criterion is needed that indicates when to stop. ... Duff, I.S., Erisman, A.M., Reid, J.K.: Direct Methods for Sparse Matrices. ... Varga, R.S.: Matrix Iterative Analysis, 2nd edn.*

**Author**: Reijer Idema

**Publisher:** Springer

**ISBN:** 9789462390645

**Category:** Mathematics

**Page:** 110

**View:** 685

*Richard Varga's Matrix Iterative Analysis [330] is an elegant introduction to the classical iterative methods. Textbooks The first textbook devoted exclusively to modern numerical linear algebra was Fox's Introduction to Numerical ...*

**Author**: G. W. Stewart

**Publisher:** SIAM

**ISBN:** 9780898714142

**Category:** Mathematics

**Page:** 458

**View:** 107

*Saad, Y. (1982b) 'Projection methods for solving large sparse eigenvalue problems', in Matrix Pencils, P. Havbad, ... Varga, R. S. (1962) Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ. von Neumann, J. (1945—6) 'A model ...*

**Author**: Francoise Chatelin

**Publisher:** SIAM

**ISBN:** 1611972469

**Category:** Eigenvalues

**Page:** 410

**View:** 225

*The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and ...*

**Author**: Maxim A. Olshanskii

**Publisher:** SIAM

**ISBN:** 9781611973464

**Category:** Mathematics

**Page:** 244

**View:** 936

*A Brief Introduction to Numerical Analysis. Birkhauser. (One citation at page 78.) [524] Tyrtyshnikov, E. E. and N. L. Zamarashkin (1998). Spectra of multilevel Toeplitz matrices: advanced theory via simple matrix relationships.*

**Author**: Daniele Bertaccini

**Publisher:** CRC Press

**ISBN:** 9781498764179

**Category:** Mathematics

**Page:** 354

**View:** 495

*H. C. Elman, Iterative methods for linear systems, in Advances in Numerical Analysis, Vol III: Large Scale Matriz Problems and the ... An iterative solution method for linear systems of which the coefficient matrix is a symmetric ...*

**Author**: D F Griffiths

**Publisher:** World Scientific

**ISBN:** 9789814498784

**Category:** Mathematics

**Page:** 380

**View:** 607

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