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 .
In Example 1, we evaluate normwise, mixed, and componentwise condition numbers for different tridiagonal matrix
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:
Before constructing the homotopy function, the symmetric square matrix B should be transformed to the symmetric tridiagonal matrix
A by the Householder transformation .
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.