Call for help to those who are good at symbolic math and/or algorithm construction (especially those who work w/ filters)

[Mike Solomon]

Hey lilypond developers,
    I have an algorithm I'm working on for my waveform patch and I am not
good (or patient) enough at symbolic math to make any headway w/ it.  In the
attached python file (which needs numpy to run), line 106 uses linalg.solve
to solve a system of equations with fairly regular properties (all of which
are commented in the code).  I have a hunch that there is a way to describe
the results of this algorithm (discounting the first len(B) values, which
are lagrangian multipliers) as a sequence (in open or closed form) using
array A & B 's constituent members as well as their lengths (which are the
same, meaning that len(A) = len(B)).  Knowing this would save the pain of
using traditional linear algebra solvers, which for a 23x23 matrix is ok,
but for a 100000x100000 matrix gets cumbersome.

Thank you in advance to any takers who want to help me with this!!!

~Mike

P.S. Extra brownie points to anybody who devises a
not-too-computationally-expensive-to-solve constraint that guarantees only
positive values for all elements of the result vector ranging from len(B) to
len(B)+len(A) (the from 0 to len(B) are lagrangian multipliers).

P.P.S. Double extra brownie points for anyone who can state the algorithm in
continuous form.  My intuition tells me that it would be some sorta
convolution between a periodic signal (see matrix IV) and several impulses
(see matrix III) with different heights (see matrix II).

system4.py
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