Tridiagonal matrix algorithm - TDMA (Thomas algorithm)
From CFD-Wiki
Introduction
The Thomas Algorithm is a special form of Gaussian elimination that can be used to solve tridiagonal systems of equations. When the matrix is tridiagonal, the solution can be obtained in operations, instead of . Example of such matrices are matrices arising from discretization of 1D problems.
We can write the tri-diagonal system in the form:
Where and
Algorithm
- for k:= 2 step until n do
-
- end loop (k)
- then
-
- for k := n-1 stepdown until 1 do
-
- end loop (k)
References
- Conte, S.D., and deBoor, C. (1972), Elementary Numerical Analysis, McGraw-Hill, New York..
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