| Description |
1 online resource (xv, 487 pages) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Studies in computational mathematics ; 15 |
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Studies in computational mathematics ; 15.
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| Summary |
The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type of problem and its description of when a given algorithm succeeds or fails. The book contains applications in several areas of applied sciences including mathematical programming and mathematical economics. There is also a huge number of exercises complementing the theory. - Latest convergence results for the iterative methods - Iterative methods with the least computational cost - Iterative methods with the weakest convergence conditions - Open problems on iterative methods. |
| Contents |
1. Linear Spaces -- 2. Monotone convergence -- 3. Contractive Fixed Point Theory -- 4. Solving Smooth Equations -- 5. Newton-like methods -- 6. More Results on Newton's Method -- 7. Equations with Nonsmooth Operators -- 8. Applications of the weaker version of the Newton-Kantorovich theorem -- 9. The Newton-Kantorovich Theorem and Mathematical Programming -- 10. Generalized equations -- 11. Monotone convergence of point to set-mapping -- 12. Fixed points of point-to-set mappings -- 13. Special topics -- Bibliography -- A Glossary of Symbols -- Index. |
| Bibliography |
Includes bibliographical references and index. |
| Note |
Print version record. |
| Language |
English. |
| Subject |
Iterative methods (Mathematics)
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Itération (Mathématiques)
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MATHEMATICS -- Numerical Analysis.
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Iterative methods (Mathematics) (OCoLC)fst00980827
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Funktionalanalysis
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Iteration
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Numerische Mathematik
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| Genre/Form |
Lehrbuch.
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| Other Form: |
Print version: Argyros, Ioannis K. Computational theory of iterative methods. Amsterdam ; London : Elsevier, 2007 9780444531629 0444531629 (OCoLC)124959845 |
| ISBN |
9780444531629 |
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0444531629 |
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9780080560700 (electronic bk.) |
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0080560709 (electronic bk.) |
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1281189189 |
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9781281189189 |
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9786611189181 |
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6611189181 |
| Standard No. |
AU@ 000043178528 |
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CHNEW 001007528 |
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DEBBG BV036962167 |
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DEBBG BV039830473 |
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DEBBG BV042307028 |
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DEBSZ 287021726 |
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DEBSZ 482358092 |
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NZ1 12541687 |
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AU@ 000055709758 |
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