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Math Help - tridiagonal system

  1. #1
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    tridiagonal system

    I need a method for solving a linear system (x1..xn) of type

    x1*(k11+k12/(x1+x2+..xn)) x2*k13 x3*k14 ....
    ... x2*(k22+k23/(x1+x2+..xn)) x3*k24 ....
    ... ..... x3*(k34+k35/(x1+x2+..xn)) x4*k36


    and so on, size about 400 x 400 elements,
    I am unable to find a solution with Thomas or similar efficient methods
    cause diagonal elements contains 1/(x1+x2+...+xn) which require separate processing,
    what am I missing here ?
    Is there a simple solution for these systems ?
    Thanks for help.
    Last edited by celi; April 16th 2014 at 11:22 PM.
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  2. #2
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    Re: tridiagonal system

    I am afraid that the question is not clear due to bad formatting so I'll to explain a bit better
    (sorry for double post)

    I need a method for solving a linear system (x1..xn) of type
    A*x=B
    where A is a tridiagonal matrix

    x x
    . x x x
    . . x x x

    with (generic) structure

    first row
    x1*(k11+k12/(x1+x2+..xn) x2*k13

    second row
    x2*k21 x3*(k22+k23/(x1+x2+..xn) x4*k24

    and so on, size N about 400 x 400 (sparse),
    I am unable to find a solution which allow to use Thomas or similar efficient methods
    cause diagonal elements contains K/(x1+x2+...+xn) which require separate processing,
    what am I missing here ?
    Is there any simple solution for these systems ?
    Thanks for help.
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  3. #3
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    Re: tridiagonal system

    you keep calling this a linear system. It is not.
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  4. #4
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    Re: tridiagonal system

    thanks for the comment, I appreciate any contribute,
    actually I convert values to fractions (by preprocessing) and the solution is very slow,
    a very efficient iterative system could be acceptable (or provide comparable timing)
    how do you suggest to solve such system ?
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  5. #5
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    Re: tridiagonal system

    Toying with this it becomes clear that the whole thing is a quadratic form.

    Have you tried rewriting the whole thing as a quadratic form and applying some algorithm for solving the quadratic system?

    This paper for example
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  6. #6
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    Re: tridiagonal system

    thanks for the contribute,
    a iterative procedure would appear interesting providing there is a efficient way to correct vector x1..xn at each step,
    actually this is the area where my resources show the limits...
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