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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 round-off 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 10d 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 ill-conditioned matrix and a matrix with a low condition number is referred to a well-conditioned 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 |