Engineering and Scientific Subroutine Library for AIX Version 3 Release 3: Guide and Reference

Linear Least Squares Considerations

This section provides some key points about using the linear least squares subroutines.

Use Considerations

If you want to use a singular value decomposition method to compute the minimal norm linear least squares solution of AX is congruent to B, calls to SGESVF or DGESVF should be followed by calls to SGESVS or DGESVS, respectively.

Performance and Accuracy Considerations

1. Least squares solutions obtained by using a singular value decomposition require more storage and run time than those obtained using a QR decomposition with column pivoting. The singular value decomposition method, however, is a more reliable way to handle rank deficiency.
2. The short-precision subroutines provide increased accuracy by accumulating intermediate results in long precision. Occasionally, for performance reasons, these intermediate results are stored.
3. The accuracy of the resulting singular values and singular vectors varies between the short- and long-precision versions of each subroutine. The degree of difference depends on the size and conditioning of the matrix computation.
4. There are ESSL-specific rules that apply to the results of computations on the workstation processors using the ANSI/IEEE standards. For details, see What Data Type Standards Are Used by ESSL, and What Exceptions Should You Know About?.