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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Solution of Nonlinear Equations
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algorithm assume B-splines best approximation bisection method coefficients column Computer Problem continued fraction continuous convergence convex set cubic spline defined denoted derivatives Determine differential equation divided difference eigenvalues elements example factorization Find formula Gaussian elimination given grid Hence inequality initial-value problem inner product inner-product space integral interpolating polynomial interval inverse iteration knots Lemma lower triangular machine numbers mathematical matrix norm n x n matrix Newton's method nodes nonsingular nonzero numerical solution obtain orthogonal orthonormal polynomial of degree positive definite preceding problem procedure Prove pseudoinverse quadratic real number result roots 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's Theorem THEOREM 1 Theorem truncation error two-point boundary-value problem upper triangular values variables vector write zero