
MATRIX CONDITION NUMBERName:
For each of these, the condition number gives a bound on the accuracy that can be obtained (this does not include the effects of roundoff error, algorithm choice, or the floating point accuracy of the computer) for finding the matrix inverse, the determinant, or solving a system of equations. A rule of thumb is that if the condition number is approximately 10^{d} then the elements of the LU decomposed matrix generally have d fewer significant digits than the original matrix. A matrix with high condition numbers are referred to as illconditioned matrix and a matrix with a low condition number is referred to a wellconditioned matrix. Some analysts prefer to use the reciprocal of the condition number (see Syntax 2 below).
<SUBSET/EXCEPT/FOR qualification> where <mat1> is a matrix for which the condition number is to be computed; <par> is a parameter where the resulting condition number is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional (and rarely used in this context).
<SUBSET/EXCEPT/FOR qualification> where <mat1> is a matrix for which the reciprocal of the condition number is to be computed; <par> is a parameter where the resulting reciprocal of the condition number is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional (and rarely used in this context).
LET C = MATRIX RECIPROCAL CONDITION NUMBER A
DIMENSION 100 COLUMNS READ MATRIX X 16 16 19 21 20 14 17 15 22 18 24 23 21 24 20 18 17 16 15 20 18 11 9 18 7 END OF DATA LET C = MATRIX CONDITION NUMBER X LET RC = MATRIX RECIPROCAL CONDITION NUMBER X PRINT C RCThe following output is generated. C  31.82 RC  0.03
Date created: 09/14/2011 