Numerical analysis: mathematics of scientific computing
This highly successful and scholarly book introduces readers 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 this book apart from the authors' well-respected and best-selling text: NUMERICAL MATHEMATICS AND COMPUTING, FOURTH EDITION.
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algorithm assume best approximation bisection method characteristic curves coefficients column Computer Problem continuous continuous function convergence convex convex set cubic spline defined denoted derivatives determine differential equation divided difference eigenvalues elements Equation 11 Equation 9 Euler's method example factorization Find formula function f(x Gaussian elimination given grid Hence inequality initial-value problem inner product inner-product space integral interpolating polynomial interval inverse iteration knots Lemma linear function lower triangular machine numbers mathematical matrix norm Newton's method nodes nonsingular nonzero notation numerical solution obtain orthonormal polynomial of degree positive definite procedure Prove pseudoinverse real number result roundoff error Runge-Kutta Runge-Kutta method satisfy secant method Section sequence Show singular-value decomposition solve space step subspace Suppose system of equations Taylor series Taylor-series method Taylor's Theorem truncation error two-point boundary-value problem upper triangular values variables vector zeros