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Numerical Mathematics and Applications

1st Edition, Volume 1 - November 1, 1986

Editors: J. Vignes, R. Vichnevetsky

Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 9 5 6 7 - 1

IMACS Transactions on Scientific Computation – 85, Volume I: Numerical Mathematics and Applications contains papers on theoretical and applied aspects of numerical mathematics… Read more

Numerical Mathematics and Applications

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IMACS Transactions on Scientific Computation – 85, Volume I: Numerical Mathematics and Applications contains papers on theoretical and applied aspects of numerical mathematics presented at the 11th IMACS World Congress on Scientific Computation, held in Oslo, Norway on August 5-9, 1985. The book focuses on the processes, methodologies, and approaches involved in computer arithmetic. The selection first highlights the use of CESTAC method in the parallel computation of roots of polynomials, CESTAC, and reducing abbreviation errors in iterative resolution of linear systems. Discussions focus on notations and theoretical processes, sequence of iterates in floating-point arithmetic, perturbation method, and CESTAC tested on algorithm and numerical results. The book then takes a look at optimal termination criterion and accuracy tests in mathematical programming; use of the normed residue to check the quality of the solution of a linear system; and computable bounds for solutions of integral equations. The manuscript examines arbitrarily accurate boundaries for solutions of ODEs with initial values using variable precision arithmetic and remarks on some modified Romberg algorithms for numerical integration. Topics include speed of convergence and a priori truncation error estimates, acceleration of convergence, extrapolation schemes, and the initial boundary value problem. The selection is a dependable source of data for mathematicians and researchers interested in numerical mathematics and applications.