Theory and Applications of Numerical Analysis
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.
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Chapter 4 The interpolating polynomial
Chapter 5 Best approximation
Chapter 6 Splines and other approximations
Chapter 7 Numerical integration and differentiation
Chapter 8 Solution of algebraic equations of one variable
Chapter 9 Linear equations
Chapter 10 Matrix norms and applications
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accuracy algorithm calculate Chapter Chebyshev polynomials Chebyshev series choose coefficients column compute consider construct contraction mapping corrector decimal places deduce defined denote derivatives diagonal difference equation differential equation digits divided difference eigenvalues eigenvectors elements elimination method equally spaced error bound estimate Euler's method evaluate Example exists factorization formula function f give given Hence initial value problem integral interpolating polynomial interval inverse iterative method least squares approximations Lemma linear equations matrix maximum minimax approximation multiples n x n Newton’s method non-singular non-zero norm Note obtain orthogonal orthogonal polynomials pivoting polynomial of degree proof real numbers recurrence relation replace result right side root rounding errors Runge–Kutta method satisfies secant method second order Section sequence Show solve spline Suppose symmetric symmetric matrix Table Taylor polynomial Taylor series Theorem trapezoidal rule tridiagonal unique solution vector verify write zero