Moscow : Mir Publishers, 1987 - Numerical analysis - 688 pages
Approximate computations and error estimation in performing computations; Computing the values of functions; Numerical solution of systems of linear algebraic equations; Numerical solution of systems of nonlinear equations; The interpolation of functions; numerical differentiation; Approximate computation of integrals; Approximate solution of ordinary differential equations; Boundary value problems for ordinary differential equations; Numerical solution of equations with partial derivaties and of integral equations; Appendices; Answers; References.
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Numerical Recipes in C: The Art of Scientific Computing, Book 4
William H. Press
Limited preview - 1992
INTRODUCTION GENERAL RULES OF COMPUTATIONAL WORK
Basic sources of errors
34 other sections not shown
accuracy algebraic equation approximate number approximate value assume coefficients column complex roots computations constant terms continued fraction convergence Corollary correct digits corresponding Definition derivative diagonal eigenvalues eigenvectors elements equal estimate Example finite differences follows Fourier series function f(x given Hence holds true Horner scheme inequality initial vector integral interpolation formula interval inverse matrix iteration process limiting absolute error limiting relative error linear system linear transformation linearly linearly independent matrix series method of iteration modulus Monte Carlo method multiplying Newton's method nonsingular nonsingular matrix Note number of correct obtain orthogonal orthogonal matrix points positive roots process of iteration Proof quadrature formula random numbers real roots relative error remainder term roots of equation scheme Seidel process sequence significant digits Solution solving space Sturm sequence successive approximations Suppose Theorem tion variable whence zero