By Ulrich W. Kulisch, Willard L. Miranker
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Extra resources for A New Approach to Scientific Computation
Is non-singular do we have an xeX with Ax = b. o^XeffVJR. Moreover, only if R The two problems are solved by the next theorem (cf. ). T h e o r e m 2 . 1 : Let A,ReMJR and beVJR.
Result of the new algorithm : No inclusion could be computed. 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.
In any case the computer verifies that the matrix of the linear system has maximum rank (if this is true) without any effort on the part of the user. The condition number of the Hilbert 15x15 matrix is approximately 10**22. It is the Hilbert matrix with largest number of rows which is exactly storable with 12 decimal digit accuracy. Despite the ill-condition of the system the solution is included with least significant bit accuracy. 35 Computer Demonstration Packages Inversion of a matrix This package computes an inclusion of the inverse of a real or interval matrix.