Links in the text refer to the lower part of the page
contains three matrix containers (value arrays):
A, B and X. Mathgrapher handles real matrices only. The results (eigenvalues, eigenvectors)
may be complex. The screen view show the operations that can be performed on these matrices:
The solution is computed to the real linear least squares
minimize ||AX-B|| where A is a m x n matrix which may be rank-deficient.
Suppose you have a number of measurements B(ti), where you expect that B is the result of
a linear combination of functions (or data sets):
A and B are known and we want to find C (=X) for which ||AC-B|| is minimized.
Let's assume that c1=1, c2=2, c3=3, c4=4 and calculate B for t=0, 0.5, 1.0, 1.5, 2.0, 2.5,
When the Go button is pushed the following solution for C (or X) is found.
The results are given in the matrix X. The results are also written in the
Results.out file and shown in the results window.
Note that A may also contain columns that represent data sets instead of functions.
The least squares algorithm used here is also used in the Curve fit module (linear
least squares fit to a combination of functions and Data sets.