Numerical analysis 2nd Edition by Walter Gautschi ISBN 0817682589 978-0817682583
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Product details:
ISBN 10: 0817682589
ISBN 13: 978-0817682583
Author: Walter Gautschi
Revised and updated, this second edition of Walter Gautschi’s successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. 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 edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.
Table of contents:
1. Machine Arithmetic and Related Matters
1.1 Real Numbers, Machine Numbers, and Rounding
1.1.1 Real Numbers
1.1.2 Machine Numbers
1.1.3 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
2. Approximation and Interpolation
2.1 Least Squares Approximation
2.1.1 Inner Products
2.1.2 The Normal Equations
3. Polynomial Interpolation
3.1 Algebraic Formulation
3.1.1 Uniqueness of the Interpolating Polynomial
3.1.2 Error in Polynomial Interpolation
3.1.3 Applications
3.2 Newton Form of the Interpolating Polynomial
3.2.1 Divided Differences
3.2.2 Newton Form of the Polynomial
3.3 Lagrange Form of the Interpolating Polynomial
3.3.1 Barycentric Form
3.4 Interpolation at Chebyshev Points
3.5 Hermite Interpolation
3.6 Spline Interpolation
3.6.1 Linear Splines
3.6.2 Quadratic Splines
3.6.3 Cubic Splines
3.7 Notes to Chapter 3
Exercises and Machine Assignments to Chapter 3
Exercises
Machine Assignments
Selected Solutions to Exercises
Selected Solutions to Machine Assignments
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