Linear Least Squares (LLS) Problems

The **linear least squares problem** is:

In the most usual case and , and in this case the solution to problem (2.1) is unique, and the problem is also referred to as finding a

When and , there are an infinite number of solutions which exactly satisfy . In this case it is often useful to find the unique solution which minimizes , and the problem is referred to as finding a

The driver routine LA_GELS solves problem (2.1) on the assumption that -- in other words, has

In the general case when we may have -- in other words, may be

The driver routines LA_GELSY, LA_GELSS, and LA_GELSD, solve this general formulation of problem (2.1), allowing for the possibility that is rank-deficient; LA_GELSY uses a

The subroutine LA_GELSD is significantly faster than its older counterpart LA_GELSS, especially for large problems, but may require somewhat more workspace depending on the matrix dimensions.

The LLS driver routines are listed in Table 2.3.

All four routines allow several right hand side vectors and corresponding solutions to be handled in a single call, storing these vectors as columns of matrices and , respectively. Note however that problem (2.1) is solved for each right hand side vector independently; this is