A First Course in Numerical AnalysisCourier Corporation, 1 gen 2001 - 606 pagine 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. |
Sommario
INTRODUCTION AND PRELIMINARIES | 1 |
APPROXIMATION AND ALGORITHMS | 31 |
INTERPOLATION | 52 |
NUMERICAL DIFFERENTIATION NUMERICAL QUADRATURE AND SUMMATION | 89 |
THE NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS | 164 |
FUNCTIONAL APPROXIMATION LEASTSQUARES TECHNIQUES | 247 |
FUNCTIONAL APPROXIMATION MINIMUM MAXIMUM ERROR TECHNIQUES | 285 |
THE SOLUTION OF NONLINEAR EQUATIONS | 332 |
THE SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS | 410 |
THE CALCULATION OF EIGENVALUES AND EIGENVECTORS OF MATRICES | 483 |
Altre edizioni - Visualizza tutto
A First Course in Numerical Analysis Anthony Ralston,Philip Rabinowitz Visualizzazione estratti - 1978 |
Parole e frasi comuni
a₁ a₂ abscissas accuracy algebra algorithm applied arithmetic assume b₁ bound c₁ calculate Chebyshev Chebyshev polynomials coefficients column consider convergence corrector corresponding deduce defined derive diagonal difference digital computer discussed eigenvalues eigenvectors elements error term estimate evaluate Example floating-point Gaussian elimination given H₁ Hessenberg Householder's method interpolation formula interval inverse iterative methods Jacobi method k₁ magnitude Math mathematical matrix maximum error multiplications Newton-Cotes Newton-Cotes formulas norm numerical analysis numerical integration orthogonal P₁ Padé approximations polynomial of degree problem QR algorithm quadrature formula r₁ rational function right-hand side roots roundoff error Runge-Kutta methods satisfies secant method sequence Show solve stability subintervals symmetric symmetric matrix tabular points theorem tion transformation trapezoidal rule triangular tridiagonal true value truncation error vector w₁ x₁ Xi+1 y₁ Yn+1 zero