Before constructing the homotopy function, the symmetric square matrix B should be transformed to the symmetric tridiagonal matrix
A by the Householder transformation .
Realizations of this method for symmetric tridiagonal matrix
can be found, for instance, in the monograph [9, Section 8.
The coefficient matrix [M] is not a tridiagonal matrix
, so it cannot be solved with the efficient forward-elimination and backward- substitution method directly.
Above algebraic equations are in tridiagonal matrix
form which is solved by using LU decomposition in the present work.
For example, Deift and Nanda  discussed an inverse eigenvalue problem of a tridiagonal matrix
under a submatrix constraint; Peng and Hu  considered an inverse eigenpair problem of a Jacobi matrix under a leading principal submatrix constraint; Peng and Hu  studied a inverse problem of bi-symmetric matrices with a leading principal submatrix constraint, for more we refer the reader to [6, 12, 24].
The terms of the matrix K is a tridiagonal matrix
of 2 x 2 submatrices and the determinant can be easy evaluated for any value of k and a fixed [omega].
1999] are designed to find all the eigenvalues of a symmetric tridiagonal matrix
in a specified interval.
Then the shifts are introduced and the tridiagonal matrix
When A is symmetric or Hermitian, the Arnoldi process reduces to the Lanczos algorithm, in which the matrix H is a symmetric tridiagonal matrix
If B2 = 1 then, on exit, the main diagonal and the subdiagonal of the resulting tridiagonal matrix
m+1,m] is a symmetric tridiagonal matrix
, and if [mu] is an eigenvalue of [B.
with a tridiagonal matrix
B with 2's on the diagonal and -1's on the subdiagonals and C is a matrix with all entries zero except for a 1 in the lower left corner.