[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
## Re: solving Ax=b

**From**: |
A S Hodel |

**Subject**: |
Re: solving Ax=b |

**Date**: |
Sat, 4 Jan 2003 07:04:21 -0600 |

`For your problem I suspect that "easy" is a relative term (like NASA's
``goal of "low-cost" access to space).
`

`There are numerous iterative methods for large, sparse A x = b
``problems. Most of these will require work on your part. See Golub and
``Van Loan, "Matrix Computations," Johns-Hopkins University press, for an
``introduction to some of them.
`

`As a starting point, you may wish to look at the GMRES method by Youcef
``Saad (I think this is published in SIAM J. Sci. Stat. Comput. 1986).
``The octave routine krylov may be a useful starting point, but you'll
``have to modify it to use your f(A,x) instead of A*X. If you can look at
``other splittings A = M + N besides M= I, N = (A-I), then some of Gene
``Wachspress's ADI (Alternating Direction Implicit) methods of the 60's
``may be of use. I haven't kept up with the latest and greatest very
``large sparse solver methods, so I'd suggest a visit to the last few
``years of SIAM J. Matrix Analysis and SIAM J. Sci Stat Comput. to see
``what you can find.
`
On Saturday, January 4, 2003, at 03:00 AM, Sven Khatri wrote:

Hi All,
I'm looking to solve a problem that is equivalent to solving for x in
the system of linear equations:
Ax = b
where A \in R^{n \times n}, x \in R^n, b \in R^n. But the catch is
that n is too large to explicitly construct A (even in Matlab's sparse
implementation) but I can construct a function f so that f(x) = Ax. Is

`there an easy way (within octave) to solve for x? I can solve the
``problem
`by introducing \tilde{A} = I - A, so that the solution to
x = \tilde{A}x + b
is a solution to the above problem and \tilde{A} is a contraction and
solving the problem iteratively but this computation is VERY slow.
thanx...
Sven
PS I hope you all are comfortable with the above latex notation
-------------------------------------------------------------
Octave is freely available under the terms of the GNU GPL.
Octave's home on the web: http://www.octave.org
How to fund new projects: http://www.octave.org/funding.html
Subscription information: http://www.octave.org/archive.html
-------------------------------------------------------------

-------------------------------------------------------------
Octave is freely available under the terms of the GNU GPL.
Octave's home on the web: http://www.octave.org
How to fund new projects: http://www.octave.org/funding.html
Subscription information: http://www.octave.org/archive.html
-------------------------------------------------------------

**solving Ax=b**, *Sven Khatri*, `2003/01/04`
**Re: solving Ax=b**,
*A S Hodel* **<=**