Numerical Analysis: Mathematics of Scientific ComputingAmerican Mathematical Soc., 2009 - 788 pagine This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations and careful proofs. In an engaging and informal style, the authors demonstrate that many computational procedures and intriguing questions of computer science arise from theorems and proofs. Algorithms are presented in pseudocode, so that students can immediately write computer programs in standard languages or use interactive mathematical software packages. This book occasionally touches upon more advanced topics that are not usually contained in standard textbooks at this level. |
Sommario
What Is | 1 |
Computer Arithmetic | 37 |
Solution of Nonlinear Equations | 73 |
Solving Systems of Linear Equations | 139 |
Selected Topics in Numerical Linear Algebra | 254 |
Approximating Functions | 308 |
Numerical Differentiation and Integration | 465 |
Numerical Solution of Ordinary | 524 |
Numerical Solution of Partial Differential Equations | 615 |
Linear Programming and Related Topics | 681 |
Optimization | 711 |
Appendix A An Overview of Mathematical Software | 731 |
Altre edizioni - Visualizza tutto
Numerical Analysis: Mathematics of Scientific Computing David Ronald Kincaid,Elliott Ward Cheney Visualizzazione estratti - 2002 |
Numerical Analysis: Mathematics of Scientific Computing David Ronald Kincaid,Elliott Ward Cheney Visualizzazione estratti - 1991 |
Numerical Analysis: Mathematics of Scientific Computing David Ronald Kincaid,Elliott Ward Cheney Anteprima non disponibile - 2009 |
Parole e frasi comuni
algorithm assume B-splines best approximation bisection method coefficients column COMPUTER PROBLEMS continued fraction continuous convergence convex set cubic spline defined denoted derivatives Determine diagonal differential equation divided difference eigenvalues elements EXAMPLE 1 Solution factorization Find formula function f Gaussian elimination given Hence inequality initial-value problem inner product inner-product space integral interpolates f interpolating polynomial interval inverse iteration knots Lemma lower triangular m x n machine numbers mathematical matrix norm n x n matrix Newton Newton's method nodes nonsingular nonzero numerical solution obtain orthonormal output polynomial of degree preceding problem procedure Prove pseudoinverse quadratic real number result roots roundoff error Runge-Kutta method satisfy secant method Section sequence Show singular-value decomposition solve space step subspace Suppose system of equations Taylor series Taylor's Theorem truncation error upper triangular values variables vector write xn+1 zero