Matrix Division on the 28C/S (and later)

[J-F Garnier]

(02-25-2020 08:16 PM)John Keith Wrote:  AFAIK, the "/" key essentially inverts the matrix containing the equations then multiplies the inverted matrix by the array of values. The HP-48 manual does say that it uses 15 digit internal precision and is more accurate than inversion followed by multiplication.

(02-26-2020 08:44 AM)Werner Wrote:  No, it doesn't. It solves the system A*X=B, returning X, without having to calculate the inverse.
While mathematically solving A*X=B and calculating X=inv(A)*B are equivalent, numerically they are not.

Hi Werner, can you elaborate on this?
I always thought (and still think) that solving A*X=B is done by inverting A. It may exist other numerical methods, iterative or so, but I don't think HP is using such methods.
So I'm interested to get some justification of your point.

An indication: on Basic machines (Series 80, 75, 71), the MAT ... SYS statement is using matrix inversion, according to the manuals, and provides the determinant for the DETL function (last DET computed in INV or SYS statements).

J-F