Overview

There is some excess baggage in this field in NAG, since it distinguishes approximate from accurate routines. The approximation is not in the analytical, but in the numeric sense.

Leaving F04QAF aside, the need is for:

• A matrix inverter (F04AAF is used only as an inverter).
• A solver for A * x = b where A is square and x and b are vectors. The problem A * X = B where A is n by n, X and B are n by m, can be split into m problems A * x = b all with the same A.
• The third need is a least-squares solver for A * x = b where A is not square and b has more dimensions than x.

Looking at SLATEC, four routines are needed. PDA_DGEDI computes the determinant and/or inverse of a matrix, but must be preceded by a factoriser, namely PDA_DGEFA. PDA_DGEFS solves A * x = b where A is square. It can re-use a factorisation of A from a previous run, and in that sense supports the solution of A * X = B. Finally, PDA_DBOLS solves the over-determined problem A * x = b in the least-squares sense.