Re: Slow LinearSolve.
- To: mathgroup at smc.vnet.net
- Subject: [mg49684] Re: Slow LinearSolve.
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Tue, 27 Jul 2004 07:01:37 -0400 (EDT)
- Organization: The University of Western Australia
- References: <ce2gcm$8tu$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <ce2gcm$8tu$1 at smc.vnet.net>,
Aaron Fude <aaronfude at yahoo.com> wrote:
> Within 24 hours and counting, Mathematica was not able to solve Ax = b for
> the following A and the following B. Another system does this in a matter of
> seconds.
The other system does it numerically, I assume? Mathematica is trying to
compute the answer exactly. If you enter
LinearSolve[N[A], b]
and you will get an answer immediately.
I note that your matrix A is a Vandermonde matrix
Table[Exp[I n m Pi/12], {m, -6, 6}, {n, 0, 12}] == A
or
x[m_] = Exp[I m Pi/12]
Table[x[m]^n, {m, -6, 6}, {n, 0, 12}] == A
(see http://mathworld.wolfram.com/VandermondeMatrix.html) and the system you
want to solve is related to computing the (inverse) discrete Fourier
transform of b.
Cheers,
Paul
> How do make Mathematica do the same? I use "LinearSolve[A, b]"
>
> A = {{1, -I, -1, I, 1, -I, -1, I, 1, -I, -1, I, 1}, {1, E^(((-5*I)/12)*Pi),
> E^(((-5*I)/6)*Pi),
> E^(((3*I)/4)*Pi), E^((I/3)*Pi), E^((-I/12)*Pi), -I, E^(((-11*I)/12)*Pi),
> E^(((2*I)/3)*Pi),
> E^((I/4)*Pi), E^((-I/6)*Pi), E^(((-7*I)/12)*Pi), -1},
> {1, E^((-I/3)*Pi), E^(((-2*I)/3)*Pi), -1, E^(((2*I)/3)*Pi), E^((I/3)*Pi), 1,
> E^((-I/3)*Pi),
> E^(((-2*I)/3)*Pi), -1, E^(((2*I)/3)*Pi), E^((I/3)*Pi), 1},
> {1, E^((-I/4)*Pi), -I, E^(((-3*I)/4)*Pi), -1, E^(((3*I)/4)*Pi), I,
> E^((I/4)*Pi), 1,
> E^((-I/4)*Pi), -I, E^(((-3*I)/4)*Pi), -1}, {1, E^((-I/6)*Pi),
> E^((-I/3)*Pi), -I,
> E^(((-2*I)/3)*Pi), E^(((-5*I)/6)*Pi), -1, E^(((5*I)/6)*Pi),
> E^(((2*I)/3)*Pi), I,
> E^((I/3)*Pi), E^((I/6)*Pi), 1}, {1, E^((-I/12)*Pi), E^((-I/6)*Pi),
> E^((-I/4)*Pi),
> E^((-I/3)*Pi), E^(((-5*I)/12)*Pi), -I, E^(((-7*I)/12)*Pi),
> E^(((-2*I)/3)*Pi),
> E^(((-3*I)/4)*Pi), E^(((-5*I)/6)*Pi), E^(((-11*I)/12)*Pi), -1},
> {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, E^((I/12)*Pi), E^((I/6)*Pi),
> E^((I/4)*Pi),
> E^((I/3)*Pi), E^(((5*I)/12)*Pi), I, E^(((7*I)/12)*Pi), E^(((2*I)/3)*Pi),
> E^(((3*I)/4)*Pi),
> E^(((5*I)/6)*Pi), E^(((11*I)/12)*Pi), -1}, {1, E^((I/6)*Pi), E^((I/3)*Pi),
> I,
> E^(((2*I)/3)*Pi), E^(((5*I)/6)*Pi), -1, E^(((-5*I)/6)*Pi),
> E^(((-2*I)/3)*Pi), -I,
> E^((-I/3)*Pi), E^((-I/6)*Pi), 1}, {1, E^((I/4)*Pi), I, E^(((3*I)/4)*Pi), -1,
> E^(((-3*I)/4)*Pi), -I, E^((-I/4)*Pi), 1, E^((I/4)*Pi), I,
> E^(((3*I)/4)*Pi), -1},
> {1, E^((I/3)*Pi), E^(((2*I)/3)*Pi), -1, E^(((-2*I)/3)*Pi), E^((-I/3)*Pi), 1,
> E^((I/3)*Pi),
> E^(((2*I)/3)*Pi), -1, E^(((-2*I)/3)*Pi), E^((-I/3)*Pi), 1},
> {1, E^(((5*I)/12)*Pi), E^(((5*I)/6)*Pi), E^(((-3*I)/4)*Pi), E^((-I/3)*Pi),
> E^((I/12)*Pi), I,
> E^(((11*I)/12)*Pi), E^(((-2*I)/3)*Pi), E^((-I/4)*Pi), E^((I/6)*Pi),
> E^(((7*I)/12)*Pi), -1},
> {1, I, -1, -I, 1, I, -1, -I, 1, I, -1, -I, 1}}
>
> b = {0, (-2*I)/5, 0, (-2*I)/3, 0, -2*I, Pi, 2*I, 0, (2*I)/3, 0, (2*I)/5, 0}
>
--
Paul Abbott Phone: +61 8 9380 2734
School of Physics, M013 Fax: +61 8 9380 1014
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