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Tridiagonal system
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+k11a/(x1+x2+..xn) x2*k13 second row x1*k21 x2*(k22+k22a/(x1+x2+..xn) x3*k23 third row x2*k32 x3*(k33+k33a/(x1+x2+..xn) x4*k34 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. |
Pardon me if this is a stupid question, but if I understand your notation it looks like you have a system of quadratic equations rather than linear equations. If you multiply through by the denominator of the diagonal terms don't you get a bunch of quadratic terms?
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thanks for the comment,
it looks like there is a quadratic contribute, my problem is to identify an efficient method for solving such kind of systems, a iterative method could be Ok providing there is a way (which I do not know) to generate accurate estimates for vector [x1..xn] |
If you want to use a linear solver, then try linearizing the system first. A Newton-Raphson procedure would probably be sufficient, at which point you could use a linear iterative solver to solve the resulting linear system.
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