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You searched IISERK - Title: African basins [electronic resource] / edited by R.C. Selley.
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Call Number
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519.4
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Author
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Stewart, G. W. (Gilbert W.)
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Title
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Afternotes goes to graduate school [electronic resource] : lectures on advanced numerical analysis : a series of lectures on advanced numerical analysis presented at the University of Maryland at College Park and recorded after the fact / G.W. Stewart.
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Publication
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Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1998.
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Material Info.
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1 electronic text (xii, 245 p.) : ill., digital file.
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Summary Note
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In this follow-up to Afternotes on Numerical Analysis (SIAM, 1996) the author continues to bring the immediacy of the classroom to the printed page. Like the original undergraduate volume, Afternotes Goes to Graduate School is the result of the author writing down his notes immediately after giving each lecture; in this case the afternotes are the result of a follow-up graduate course taught by Professor Stewart at the University of Maryland. The algorithms presented in this volume require deeper mathematical understanding than those in the undergraduate book, and their implementations are not trivial. Stewart uses a fresh presentation that is clear and intuitive as he covers topics such as discrete and continuous approximation, linear and quadratic splines, eigensystems, and Krylov sequence methods. He concludes with two lectures on classical iterative methods and nonlinear equations.
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Notes
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Includes bibliographical references (p. 233-235) and index.
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Notes
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Preface --
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Notes
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Part 1. Approximation. Lecture 1. General observations -- Lecture 2. The space C[0,1] -- Lecture 3. Chebyshev approximation -- Lecture 4. A theorem of de la ValleĢe Poussin -- Lecture 5. Discrete, continuous, and weighted least squares -- Lecture 6. Existence and uniqueness of the QR factorization -- Lecture 7. Expansions in orthogonal functions -- Lecture 8. Householder transformations -- Lecture 9. Operation counts --
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Notes
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Part 2. Linear and Cubic Splines. Lecture 10. Piecewise linear interpolation -- Lecture 11. Cubic splines --
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Notes
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Part 3. Eigensystems. Lecture 12. A system of differential equations -- Lecture 13. Real Schur form -- Lecture 14. A backward perturbation result -- Lecture 15. The inverse power method -- Lecture 16. Reduction to Hessenberg form -- Lecture 17. The implicit double shift -- Lecture 18. Rank and Schmidt's theorem --
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Notes
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Part 4. Krylov Sequence Methods. Lecture 19. Introduction -- Lecture 20. The Lanczos algorithm -- Lecture 21. Linear systems, errors, and residuals -- Lecture 22. Operation counts and storage requirements -- Lecture 23. Preconditioned conjugate gradients -- Lecture 24. Diagonally dominant matrices; Return to incomplete factorization --
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Notes
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Part 5. Iterations, Linear and Nonlinear. Lecture 25. Some classical iterations -- Lecture 26. Linear and nonlinear -- Bibliography -- Index.
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ISBN
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9781611971422 (electronic bk.)
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Subject
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Numerical analysis.
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Subject
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Discrete approximation
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Subject
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Continuous approximation
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Subject
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Linear spines
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Subject
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Quadratic spines
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Subject
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Eigensystems
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Subject
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Krylov sequence methods
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Added Entry
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Society for Industrial and Applied Mathematics.
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Date
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Year, Month, Day:01405141
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Link
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SIAM
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