Any irreducible
tridiagonal matrix is diagonally similar to a symmetric irreducible
tridiagonal matrix called the complex Jacobi matrix.
The first nontrivial
tridiagonal matrix (12) with N = 4 may represent, for example, a schematic quantum system with Hermitian-matrix interaction
For pressure field values calculation the
tridiagonal matrix algorithm was used [10].
In Example 1, we evaluate normwise, mixed, and componentwise condition numbers for different
tridiagonal matrix sizes.
where [A.sup.(a).sub.N+1] is a
tridiagonal matrix of dimension (N+1) x (N+2) with elements of jth row given by:
We note here that the whole linear system has a block diagonal matrix on the left hand side, and a block
tridiagonal matrix on the right, and this characteristic will be exploited to improve the time integration, as explained in the following section.
where D is a
tridiagonal matrix and [D.sup.T] represents the transpose of D.
Intermediate velocity field is solved by using fractional step method through the
tridiagonal matrix method (Thomas algorithm) [16, 17].
There are mainly one
tridiagonal matrix vector multiplication, many constant vector multiplications, and many vector-vector additions in the right-sided computation.
find the n x n, real, symmetric, and
tridiagonal matrix, B, such that [lambda](B) = [([[lambda].sub.i]).sup.n.sub.1] are the eigenvalues of [lambda], while [lambda]([B.sup.o]) = [([[lambda].sup.o.sub.i]).sup.n-1.sub.1] 1 are the eigenvalues of the leading principal submatrix of B, where [B.sup.o] is obtained from B by deleting the last row and column.
where B denotes a
tridiagonal matrix with dimension L + 2 and [M.sub.j] is a
tridiagonal matrix with dimension [2.sup.j]L.