Ulrich W. Kulisch, Willard L. Miranker's A New Approach to Scientific Computation PDF

By Ulrich W. Kulisch, Willard L. Miranker

ISBN-10: 0124286607

ISBN-13: 9780124286603

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Probaly the interval matrix contains an singular matrix. Enter HtSiR or Q, Enter I for general information. * S Enter dimension, * 2 Enter the matrix row by row. The dimension is 2. ♦ 941664 665857 ♦ 665857 470832 Siegfried M. Rump 36 1. 33333333333E+05 2. 65857000000E+053 2r\ii column * C 6 . 65857000000E+053 C -•? 41664000000E->-053 Enter H1S1R or Q. Enter I for general information. ♦ 0 In the first example the floating-point approximation to the inverse of the midpoint matrix of the interval input has been computed.

Further the aim is to achieve least significant bit accuracy for point problems and smallest possible bounds for problems with uncertainties in the coefficients. The algorithms presented demonstrate that even for extremely ill-conditioned problems, such as inverting the Hilbert 21 x21 matrix on a 14 hexadecimal digit computer, bounds with the least significant bit accuracy property can be found. The condition number of the 21x21 Hilbert 30 matrix is approximately 10 , and is the Hilbert matrix of largest dimension exactly storable on that computer.

Inc. on A in any form reserved. ISBN 0-12-428660-7 52 Siegfried M. Rump CONTENTS 0. Introduction 1. Computer Arithmetic Definitions of operations in spaces of numerical computation 2. Linear Systems Fixed point theorems, bounds for the solution, existence, uniqueness, residue, finiteness of algorithm, algorithm, interval systems, complex systems, complex interval systems, symmetric matrices, non-singularity of a matrix, positive definiteness, eigenvalues with positive real part, computing time, ill-conditioned examples 3.

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A New Approach to Scientific Computation by Ulrich W. Kulisch, Willard L. Miranker

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