Problems Used in Testing the Efficiency and Accuracy of the Modified Gram-Schmidt Least Squares Algorithm

摘要

In preparing 'Algorithm 544: L2A and L2B, Weighted Least Squares Solutions by Modified Gram-Schmidt with Iterative Refinement' for publication in ACM Transactions on Mathematical Software (Vol. 5, 1979), the Fortran computer program was extensively tested. This not describes the various types of problems which were used to explore the efficiency and accuracy of this algorithm. The Fortran subprograms which performed the various tests are listed in an appendix. Also listed are the data used in executing the testing routines as well as typical output form several different types of problems. Among the testing routines is one which is suitable for handling general linear least squares problems. Here, the user has the option of scaling his raw data in order to mitigate the effects of ill-conditioning.