A First Course in Numerical Analysis
This outstanding text by two well-known authors treats numerical analysis with mathematical rigor, but presents a minimum of theorems and proofs. Oriented toward computer solutions of problems, it stresses error analysis and computational efficiency, and compares different solutions to the same problem.
Following an introductory chapter on sources of error and computer arithmetic, the text covers such topics as approximation and algorithms; interpolation; numerical differentiation and numerical quadrature; the numerical solution of ordinary differential equations; functional approximation by least squares and by minimum-maximum error techniques; the solution of nonlinear equations and of simultaneous linear equations; and the calculation of eigenvalues and eigenvectors of matrices.
This second edition also includes discussions of spline interpolation, adaptive integration, the fast Fourier transform, the simplex method of linear programming, and simple and double QR algorithms. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.
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INTRODUCTION AND PRELIMINARIES
APPROXIMATION AND ALGORITHMS
NUMERICAL DIFFERENTIATION NUMERICAL QUADRATURE AND SUMMATION
THE NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
FUNCTIONAL APPROXIMATION LEASTSQUARES TECHNIQUES
FUNCTIONAL APPROXIMATION MINIMUM MAXIMUM ERROR TECHNIQUES
THE SOLUTION OF NONLINEAR EQUATIONS
THE SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS
THE CALCULATION OF EIGENVALUES AND EIGENVECTORS OF MATRICES
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