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- catalog abstract ""This is the first systematic study of best approximation theory in inner product spaces and, in particular, in Hilbert space. Geometric considerations play a prominent role in developing and understanding the theory. The only prerequisites for reading the book are some knowledge of advanced calculus and linear algebra. Throughout the book, examples and applications have been interspersed with the theory. Each chapter concludes with numerous exercises and a section in which the author puts the results of that chapter into a historical perspective. The book is based on lecture notes for a graduate course on best approximation that the author has taught for over twenty-five years."--Jacket.".
- catalog contributor b11867957.
- catalog created "c2001.".
- catalog date "2001".
- catalog date "c2001.".
- catalog dateCopyrighted "c2001.".
- catalog description ""This is the first systematic study of best approximation theory in inner product spaces and, in particular, in Hilbert space. Geometric considerations play a prominent role in developing and understanding the theory. The only prerequisites for reading the book are some knowledge of advanced calculus and linear algebra. Throughout the book, examples and applications have been interspersed with the theory. Each chapter concludes with numerous exercises and a section in which the author puts the results of that chapter into a historical perspective. The book is based on lecture notes for a graduate course on best approximation that the author has taught for over twenty-five years."--Jacket.".
- catalog description "Ch. 1. Inner Product Spaces -- Ch. 2. Best Approximation -- Ch. 3. Existence and Uniqueness of Best Approximations -- Ch. 4. Characterization of Best Approximations -- Ch. 5. The Metric Projection -- Ch. 6. Bounded Linear Functionals and Best Approximation from Hyperplanes and Half-Spaces -- Ch. 7. Error of Approximation -- Ch. 8. Generalized Solutions of Linear Equations -- Ch. 9. The Method of Alternating Projections -- Ch. 10. Constrained Interpolation from a Convex Set -- Ch. 11. Interpolation and Approximation -- Ch. 12. Convexity of Chebyshev Sets -- App. 1. Zorn's Lemma -- App. 2. Every Hilbert Space Is l[subscript 2](I).".
- catalog description "Includes bibliographical references (p. [315]-330) and index.".
- catalog extent "xv, 338 p. :".
- catalog identifier "0387951563 (alk. paper)".
- catalog isPartOf "CMS books in mathematics ; 7".
- catalog issued "2001".
- catalog issued "c2001.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "515/.733 21".
- catalog subject "Approximation theory.".
- catalog subject "Inner product spaces.".
- catalog subject "QA322.4 .D48 2001".
- catalog tableOfContents "Ch. 1. Inner Product Spaces -- Ch. 2. Best Approximation -- Ch. 3. Existence and Uniqueness of Best Approximations -- Ch. 4. Characterization of Best Approximations -- Ch. 5. The Metric Projection -- Ch. 6. Bounded Linear Functionals and Best Approximation from Hyperplanes and Half-Spaces -- Ch. 7. Error of Approximation -- Ch. 8. Generalized Solutions of Linear Equations -- Ch. 9. The Method of Alternating Projections -- Ch. 10. Constrained Interpolation from a Convex Set -- Ch. 11. Interpolation and Approximation -- Ch. 12. Convexity of Chebyshev Sets -- App. 1. Zorn's Lemma -- App. 2. Every Hilbert Space Is l[subscript 2](I).".
- catalog title "Best approximation in inner product spaces / Frank Deutsch.".
- catalog type "text".