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Numerical Analysis / by Walter Gautschi
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: Boston : Birkhäuser Boston, 2012Edition: Second EditionDescription: Online-Ressource (XXVI, 588p. 59 illus, digital)ISBN:- 9780817682590
- 519.4 23
- 518
- QA71-90
- QA297
Contents:
Summary: Preface to the Second Edition -- Preface -- Prologue -- Chapter 1. Machine Arithmetic and Related Matters -- Chapter 2. Approximation and Interpolation -- Chapter 3. Numerical Differentiation and Integration -- Chapter 4. Nonlinear Equations -- Chapter 5. Initial Value Problems for ODEs --- One-Step Methods -- Chapter 6. Initial Value Problems for ODEs --- Multi-Step Methods -- Chapter 7. Two-Point Boundary Value Problems for ODEs -- References -- Subject Index.Summary: The book reads like an unfolding story... Topics are motivated with great care and ingenuity that might be given to establishing the drive behind characters in a good novel... Clarity is never sacrificed for elegance. Above all, the pace is always lively and brisk, the writing concise, and the author never lets the exposition bog down... [The book] successfully conveys the author's interest and experience in the subject to the reader. —SIAM Review (on the First Edition) Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis textbook explores computational methods for problems arising in areas such as classical analysis, approximation theory, nonlinear equations, and ordinary differential equations. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the author has carefully developed and polished a complete solutions manual for this edition, which is available through the publisher and will serve as an exceptionally valuable resource for instructors. The text is geared to a one- or two-semester graduate course in numerical analysis for students who have a good background in calculus and advanced calculus and some knowledge of linear algebra, complex analysis, and differential equations. Previous exposure to numerical methods in an undergraduate class is desirable but not absolutely necessary.PPN: PPN: 1651224234Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
""Numerical Analysis""; ""Preface to the Second Edition""; ""Preface to the First Edition""; ""Contents""; ""Prologue""; ""P1 Overview""; ""P2 Numerical Analysis Software""; ""P3 Textbooks and Monographs""; ""P3.1 Selected Textbooks on Numerical Analysis""; ""P3.2 Monographs and Books on Specialized Topics""; ""P4 Journals""; ""Chapter 1: Machine Arithmetic and Related Matters""; ""1.1 Real Numbers, Machine Numbers, and Rounding""; ""1.1.1 Real Numbers""; ""1.1.2 Machine Numbers""; ""1.1.2.1 Floating-Point Numbers""; ""1.1.2.2 Fixed-Point Numbers""
""1.1.2.3 Other Data Structures for Numbers""""1.1.3 Rounding""; ""1.2 Machine Arithmetic""; ""1.2.1 A Model of Machine Arithmetic""; ""1.2.2 Error Propagation in Arithmetic Operations:Cancellation Error""; ""1.3 The Condition of a Problem""; ""1.3.1 Condition Numbers""; ""1.3.2 Examples""; ""1.4 The Condition of an Algorithm""; ""1.5 Computer Solution of a Problem; Overall Error""; ""1.6 Notes to Chapter 1""; ""Exercises and Machine Assignments to Chapter 1""; ""Exercises""; ""Machine Assignments""; ""Selected Solutions to Exercises""; ""Selected Solutions to Machine Assignments""
""Chapter 2: Approximation and Interpolation""""2.1 Least Squares Approximation""; ""2.1.1 Inner Products""; ""2.1.2 The Normal Equations""; ""2.1.3 Least Squares Error; Convergence""; ""2.1.4 Examples of Orthogonal Systems""; ""2.2 Polynomial Interpolation""; ""2.2.1 Lagrange Interpolation Formula: Interpolation Operator""; ""2.2.2 Interpolation Error""; ""2.2.3 Convergence""; ""2.2.4 Chebyshev Polynomials and Nodes""; ""2.2.5 Barycentric Formula""; ""2.2.6 Newton's Formula""; ""2.2.7 Hermite Interpolation""; ""2.2.8 Inverse Interpolation""
""2.3 Approximation and Interpolation by Spline Functions""""2.3.1 Interpolation by Piecewise Linear Functions""; ""2.3.2 A Basis for S10 (Î? )""; ""2.3.3 Least Squares Approximation""; ""2.3.4 Interpolation by Cubic Splines""; ""2.3.5 Minimality Properties of Cubic Spline Interpolants""; ""2.4 Notes to Chapter 2""; ""Exercises and Machine Assignments to Chapter 2""; ""Exercises""; ""Machine Assignments""; ""Selected Solutions to Exercises""; ""Selected Solutions to Machine Assignments""; ""Chapter 3: Numerical Differentiation and Integration""; ""3.1 Numerical Differentiation""
""3.1.1 A General Differentiation Formula for Unequally Spaced Points""""3.1.2 Examples""; ""3.1.3 Numerical Differentiation with Perturbed Data""; ""3.2 Numerical Integration""; ""3.2.1 The Composite Trapezoidal and Simpson's Rules""; ""3.2.2 (Weighted) Newton�Cotes and Gauss Formulae""; ""3.2.3 Properties of Gaussian Quadrature Rules""; ""3.2.4 Some Applications of the Gauss Quadrature Rule""; ""3.2.5 Approximation of Linear Functionals: Methodof Interpolation vs. Method of UndeterminedCoefficients""; ""3.2.6 Peano Representation of Linear Functionals""; ""3.2.7 Extrapolation Methods""
""3.3 Notes to Chapter 3""
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