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.
Avis des internautes - Rédiger un commentaire
Aucun commentaire n'a été trouvé aux emplacements habituels.
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
Autres éditions - Tout afficher
accuracy algorithm analysis applied approximation assume bound calculate called chapter choose coefficients column complex computation condition consider constant continuous convergence corresponding deduce defined definite derive desired determine diagonal difference differential equations discussed eigenvalues eigenvectors elements equal estimate evaluate exact Example exists expressed fact follows formula function give given initial integral interpolation interval inverse iteration less linear magnitude matrix maximum method multiplications norm Note obtain operations orthogonal particular points polynomial polynomial of degree positive possible Prob problem proof properties prove quadrature rational relation respectively result roots roundoff error rule satisfies sequence Show side solution solve stability stage step Suppose symmetric matrix technique term theorem theory tion transformation true values vector weights Yn+1 York zero