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Projection Methods for Systems of Equations
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Main description:The solutions of systems of linear and nonlinear equations occurs in many situations and is therefore a question of major interest. Advances in computer technology has made it now possible to consider systems exceeding several hundred thousands of equations. However, there is a crucial need for more efficient algorithms.The main focus of this book (except the last chapter, which is devoted to systems of nonlinear equations) is the consideration of solving the problem of the linear equation Ax = b by an iterative method. Iterative methods for the solution of this question are d...
Main description:
The solutions of systems of linear and nonlinear equations occurs in many situations and is therefore a question of major interest. Advances in computer technology has made it now possible to consider systems exceeding several hundred thousands of equations. However, there is a crucial need for more efficient algorithms.The main focus of this book (except the last chapter, which is devoted to systems of nonlinear equations) is the consideration of solving the problem of the linear equation Ax = b by an iterative method. Iterative methods for the solution of this question are described which are based on projections. Recently, such methods have received much attention from researchers in numerical linear algebra and have been applied to a wide range of problems.The book is intended for students and researchers in numerical analysis and for practitioners and engineers who require the most recent methods for solving their particular problem.
Review quote:
G. Walz
In the authors words, 'this book is mainly intended for researchers in the filed'. The reviewer would add: 'but it is also very interesting for students as well as for researchers in other fields'. I have learned a lot from this book, it is well written, it contains nice theoretical results as well as many algorithms and numerical examples. I think that it is a valuable contribution to numerical linear algebra.
Zentralblatt für Mathematik
A. Bultheel
...an excellent guide to the literature. ...In conlusion, the book is intended for researchers in the field, but can also be read by advanced students, for whom it may open opportunities for new directions of research.
Newsletter on Computational Applied Mathematics, Vol.15, No.1
...useful to anyone interested in the most recent results about this important class of methods.
Mathematical Reviews
Table of contents:
Introduction. 1. Preliminaries. 2. Biorthogonality. 3. Projection Methods for Linear Systems. 4. Lanczos-Type Methods. 5. Hybrid Procedures. 6. Semi-Iterative Methods. 7. Around Richardson's Projection. 8. System of Nonlinear Equations. Appendix. Schur's complement. Sylvester's and Schweins' identities. Bibliography. Index.
The solutions of systems of linear and nonlinear equations occurs in many situations and is therefore a question of major interest. Advances in computer technology has made it now possible to consider systems exceeding several hundred thousands of equations. However, there is a crucial need for more efficient algorithms.The main focus of this book (except the last chapter, which is devoted to systems of nonlinear equations) is the consideration of solving the problem of the linear equation Ax = b by an iterative method. Iterative methods for the solution of this question are described which are based on projections. Recently, such methods have received much attention from researchers in numerical linear algebra and have been applied to a wide range of problems.The book is intended for students and researchers in numerical analysis and for practitioners and engineers who require the most recent methods for solving their particular problem.
Review quote:
G. Walz
In the authors words, 'this book is mainly intended for researchers in the filed'. The reviewer would add: 'but it is also very interesting for students as well as for researchers in other fields'. I have learned a lot from this book, it is well written, it contains nice theoretical results as well as many algorithms and numerical examples. I think that it is a valuable contribution to numerical linear algebra.
Zentralblatt für Mathematik
A. Bultheel
...an excellent guide to the literature. ...In conlusion, the book is intended for researchers in the field, but can also be read by advanced students, for whom it may open opportunities for new directions of research.
Newsletter on Computational Applied Mathematics, Vol.15, No.1
...useful to anyone interested in the most recent results about this important class of methods.
Mathematical Reviews
Table of contents:
Introduction. 1. Preliminaries. 2. Biorthogonality. 3. Projection Methods for Linear Systems. 4. Lanczos-Type Methods. 5. Hybrid Procedures. 6. Semi-Iterative Methods. 7. Around Richardson's Projection. 8. System of Nonlinear Equations. Appendix. Schur's complement. Sylvester's and Schweins' identities. Bibliography. Index.