Theory and Applications of Numerical Analysis

Front Cover
G. M. Phillips, Peter J. Taylor
Elsevier, Jul 5, 1996 - Mathematics - 447 pages
Theory and Applications of Numerical Analysis is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included.
  • a unique blend of theory and applications
  • two brand new chapters on eigenvalues and splines
  • inclusion of formal algorithms
  • numerous fully worked examples
  • a large number of problems, many with solutions
 

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Contents

Chapter 2 Basic analysis
11
Chapter 3 Taylors polynomial and series
39
Chapter 4 The interpolating polynomial
52
Chapter 5 Best approximation
86
Chapter 6 Splines and other approximations
131
Chapter 7 Numerical integration and differentiation
160
Chapter 8 Solution of algebraic equations of one variable
196
Chapter 9 Linear equations
221
Chapter 11 Matrix eigenvalues and eigenvectors
299
Chapter 12 Systems of nonlinear equations
323
Chapter 14 Boundary value and other methods for ordinary differential equations
396
Computer arithmetic
418
Solutions to selected problems
424
References and further reading
440
Index
443
Copyright

Chapter 10 Matrix norms and applications
265

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Page 28 - If the sum of the first terms of a series can be made as large as we please by taking enough terms, the series is divergent.

About the author (1996)

George M. Phillips is Reader in Mathematics at the University of St. Andrews, UK. His longstanding collaboration in mathematics has encompassed both teaching and research. Both authors have published many papers in numerical analysis and approximation theory.

Peter J. Taylor is a retired Senior Lecturer from the University of Strathclyde, UK. His longstanding collaboration in mathematics has encompassed both teaching and research. Both authors have published many papers in numerical analysis and approximation theory.

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