Math::SolveTridiagonalSystem

Defined in: C4Computation.h

Solves a linear system having a tridiagonal coefficient matrix.

Prototype

void SolveTridiagonalSystem(int32 n, const float *a, const float *b, const float *c, const float *r, float *x);

Parameters

`n`	The size of the tridiagonal matrix M.
`a`	A pointer to the array containing the n subdiagonal entries of M. The coefficient `a[0]` does not exist and is never accessed.
`b`	A pointer to the array containing the n diagonal entries of M.
`c`	A pointer to the array containing the n superdiagonal entries of M. The coefficient `c[n - 1]` does not exist and is never accessed.
`r`	A pointer to an array of n constant values representing the vector r for which the linear system Mx = r is to be solved.
`x`	A pointer to the array in which the n solutions representing the vector x are to be returned. This may be the same pointer passed as the `r` parameter.

Description

The SolveTridiagonalSystem function solves a linear system Mx = r for which the coefficient matrix M is tridiagonal. The matrix M must be diagonally dominant to guarantee a valid solution.

The entries of the matrix M are specified as three arrays of size n containing the subdiagonal, diagonal, and superdiagonal entries arranged as follows.

M = [\begin{matrix} b [0] & c [0] & 0 & 0 & 0 & \dots \\ a [1] & b [1] & c [1] & 0 & 0 \\ 0 & a [2] & b [2] & c [2] & 0 \\ ⋮ & ⋱ & ⋱ & ⋱ \end{matrix}]