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From Al Chou <>
Subject [math] Does LU decomposition assume matrix is square?
Date Sat, 21 Jun 2003 17:55:06 GMT
I finally decided that cubic spline would be my first attempt at implementing
interpolation, partly because of the difficulty of finding an alternative
reference to NR for the Stoer & Bulirsch rational function method, partly
because I started to have doubts about the desirability of interpolation using
high-order polynomials/rationals, and partly because I think being forced to
implement tridiagonal linear systems solution is probably good for the library.
 I could go the NR route and embed the tridiagonal solver into the cubic spline
routine, but I think it's worthwhile to provide the tridiagonal solver
separately for others to use, given the frequency with which tridiagonal
systems appear (in physics anyway; am I dreaming too much to think that someone
might use this library to solve second order differential equations by finite

I happened to notice as I started to plan my work that RealMatrixImpl.solve,
which uses LU decomposition, doesn't explicitly check whether the matrix is
square before proceeding with the decomposition.  I think (but am not sure)
that LU decomposition assumes the matrix is square.  Currently it already
checks whether the vector of right-hand-sides of the equations is equal to the
number of rows in the matrix, which I think implicitly assumes that the matrix
is square (otherwise it would probably be more correct to check against the
number of columns).


Albert Davidson Chou

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