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Dataplot Vol 2 Vol 1

MATRIX CONDITION NUMBER

Name:
    MATRIX CONDITION NUMBER (LET)
Type:
    Let Subcommand
Purpose:
    Compute the condition number (or the reciprocal of the condition number) of a matrix.
Description:
    The determinant, the matrix inverse, and the solution to a system of equations are all closely related. Each of these can be calculated from the LU decomposition of a matrix.

    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).

Syntax 1:
    LET <par> = MATRIX CONDITION NUMBER <mat1>
                            <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).
Syntax 2:
    LET <par> = MATRIX RECIPROCAL CONDITION NUMBER <mat1>
                            <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).
Examples:
    LET C = MATRIX CONDITION NUMBER A
    LET C = MATRIX RECIPROCAL CONDITION NUMBER A
Note:
    Matrices for which a condition number is to be computed must have the same number of rows and columns. An error message is printed if they do not.
Note:
    Matrices are created with either the READ MATRIX, CREATE MATRIX, or the MATRIX DEFINITION command. Enter HELP READ MATRIX, HELP CREATE MATRIX, or HELP MATRIX DEFINITION for details.
Note:
    DATAPLOT uses the LINPACK routine SGECO to compute the condition number.
Default:
    None
Synonyms:
    None
Related Commands: Reference:
    Dongarra, Bunch, Moler, Stewart (1979), "LINPACK User's Guide," Siam.
Applications:
    Linear Algebra
Implementation Date:
    2011/9
Program:
     
    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 RC
        
    The following output is generated.
    C       --          31.82
    RC      --           0.03
        

Date created: 09/14/2011
Last updated: 09/14/2011
Please email comments on this WWW page to alan.heckert@nist.gov.