How do I solve some over-determined Linear Equations?
I have some linear equations:
( (v1.*x) + (v2.*y) ) * A = (v3.*z) * B
( (w1.*x) + (w2.*y) ) * A = (w3.*z) * B
v1, v2, v3, w1, w2 and w3 are known row vectors (with complex numbers)
A and B are matrices, usually with more columns than rows. (real)
x, y, z are row vectors; x known, y and z unknown.
I seek to solve for y and z.
What is the appropriate way to use Octave to solve these?
In truth each side represents a continuous function on [0,2pi] with
respect to different sets of orthogonal basis functions. The matrices A
and B are the Fourier Coefficients of these orthogonal functions, and I
can calculate as many or few as I feel inclined.