Elementary Numerical Analysis, 2nd Edition

by Kendall Atkinson (Univ. of Iowa)

• ISBN13: 9780471509998
• ISBN10: 047150999X
• Edition: 2nd
• Format: Hardcover
• Copyright: 1993-01-01
• Publisher: Wiley

Summary

Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. Now updated and revised, this significant revision features reorganized and rewritten content, as well as some new additional examples and problems. The text introduces core areas of numerical analysis and scientific computing along with basic themes of numerical analysis such as the approximation of problems by simpler methods, the construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic.

Table of Contents

Taylor Polynomials	1	(18)
The Taylor polynomial	2	(5)
The error in Taylor's polynomial	7	(6)
Polynomial evaluation	13	(6)
Computer Representation of Numbers	19	(16)
The binary number system	20	(5)
Floating-point numbers	25	(10)
Error	35	(26)
Errors: definitions, sources, and examples	36	(12)
Propagation of error	48	(5)
Summation	53	(8)
Rootfinding	61	(40)
The bisection method	62	(6)
Newton's method	68	(10)
Secant method	78	(5)
Fixed point iteration	83	(11)
Ill-behaved rootfinding problems	94	(7)
Interpolation	101	(40)
Polynomial interpolation	102	(9)
Divided differences	111	(10)
Error in polynomial interpolation	121	(8)
Interpolation using spline functions	129	(12)
Approximation of Functions	141	(20)
The best approximation problem	142	(5)
Chebyshev polynomials	147	(6)
A near-minimax approximation method	153	(8)
Numerical Integration and Differentiation	161	(44)
The trapezoidal and Simpson rules	162	(10)
Error formulas	172	(15)
Gaussian numerical integration	187	(8)
Numerical differentiation	195	(10)
Solution of Systems of Linear Equations	205	(98)
Systems of linear equations	206	(4)
Gaussian elimination	210	(15)
Matrix arithmetic	225	(13)
The LU factorization	238	(10)
Error in solving linear systems	248	(8)
Least squares data fitting	256	(12)
The eigenvalue problem	268	(14)
Iteration methods	282	(9)
Nonlinear systems	291	(12)
The Numerical Solution of Differential Equations	303	(68)
Theory of differential equations: An introduction	304	(7)
Euler's method	311	(8)
Convergence analysis of Euler's method	319	(7)
Taylor and Runge-Kutta methods	326	(13)
Multistep methods	339	(10)
Stability of numerical methods	349	(10)
Systems of differential equations	359	(12)
Appendix A Mean Value Theorems	371	(10)
Appendix B Mathematical Formulas	381	(10)
Appendix C Numerical Analysis Software Packages	391	(6)
Answers to Selected Problems	397	(20)
References	417	(4)
Index	421