Numerical Analysis: Mathematics of Scientific ComputingThis highly successful and scholarly book introduces students with diverse backgrounds to the 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 careful proofs and scientific background.An in-depth treatment of the topics of numerical analysis, a more scholarly approach, and a different menu of topics sets Numerical Analysis: Mathematics of Scientific Computing, Second Edition apart form the authors' well-respected and best-selling text: Numerical Mathematics and Computing, Fourth Edition. |
Contents
1 | 1 |
Computer Arithmetic | 39 |
Solution of Nonlinear Equations | 78 |
Copyright | |
9 other sections not shown
Common terms and phrases
A₁ algorithm assume B-splines b₁ best approximation bisection method coefficients column COMPUTER PROBLEMS continuous continuous function convergence convex convex set defined denoted derivatives determine diagonal differential equation divided difference eigenvalues elements example factorization Find formula function f Gaussian elimination given Hence inequality initial-value problem inner product inner-product space integral interpolates ƒ interval inverse iteration knots Lemma lower triangular machine numbers mathematical matrix norm Newton's method nodes nonsingular nonzero numerical solution obtain orthonormal output pivoting polynomial of degree procedure Proof Prove pseudoinverse real number result roundoff error Runge-Kutta Runge-Kutta method satisfy secant method Section sequence Show singular-value decomposition solve space step Suppose system of equations Taylor series Taylor's Theorem Theorem ti+1 truncation error u₁ upper triangular values variables vector write x₁ Xn+1 zeros