Theory and Applications of Numerical AnalysisTheory and Applications of Numerical Analysis is a selfcontained 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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Contents
11  
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 
440  
443  
Chapter 10 Matrix norms and applications  265 
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Theory and Applications of Numerical Analysis George McArtney Phillips,Peter John Taylor No preview available  1996 
Common terms and phrases
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 nonsingular nonzero 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
Popular passages
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.