This system of equations is solved using the TriDiagonal
Matrix Algorithm (Patakar, 1980).
To provide a reasonable initial guess for the iteration variables, the tridiagonal
algorithm (Seader and Henley, 1998) with the reaction term in the mole balance set to zero is used.
We know that the complexity of this method is O(n), where n is the order of the tridiagonal
N](x) are given by the eigenvalues of the N x N tridiagonal
The linear system generated is a block tridiagonal
matrix, which is solved using either a direct or iterative solver.
In addition, a set of tridiagonal
systems are solved through LU decomposition.
For an uniform periodic boundary 1-d CA, the matrix is circulant, and for nearest neighborhood null boundary 1-d CA, the matrix is tridiagonal
El ensamblaje busca una matriz bien condicionada, que permita invertirse mediante el metodo de inversion tridiagonal
independiente (Gauss-Seidel) y propio del programa.
James Wilkinson, who was responsible for many practical advances in numerical linear algebra, also sought to prove the QR algorithm for tridiagonal
matrices always converged using exact arithmetic--a very impractical result, since no one does exact arithmetic.
Furthermore, it is immediately apparent that when the matrices are not full, but possess a special structure such as tridiagonal
, contain only one nonzero row or column, etc.
i] with (22)-(24) may be written as a block tridiagonal
matrix for [([u.
To maintain the original block tridiagonal
structure also on the coarse levels, the overall number k of smoothers that can be included in both restriction and prolongation is restricted by k < g.