Function solving

Open discussion for MAGMA library (Matrix Algebra on GPU and Multicore Architectures)

Function solving

Postby resolvent » Mon Nov 05, 2012 7:27 pm

Can someone answer to this question: I have user function called f(x), is there some way to get x from equation f(x) = CONST without writing f^(-1) function? Does MAGMA provide numericall solving or something like this?
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Re: Function solving

Postby mgates3 » Tue Nov 06, 2012 2:04 pm

Yes, you can solve f(x) = c without writing the inverse f^{-1} function. I will direct you to the chapter on solving nonlinear equations in any standard scientific computing or numerical analysis text (e.g., Scientific Computing: An Introductory Survey, by Michael Heath). Newton's Method is one such method, but requires writing the derivative df(x). Broyden's Method requires only f(x), not the derivative.

If f(x) is linear, so the problem can be written as Ax=b for matrix A and vectors x and b, then MAGMA provides software to solve that. Also, one step in implementing Newton's or Broyden's Method is to solve a linear system of equations, which again, MAGMA can do.

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