This also means that for any irreducible tridiagonal
matrix [T.sub.n], there exists a linear functional C quasi-definite on [P.sub.n-1] such that [T.sub.n] is determined by the first 2n moments of C.
Table 1: Condition numbers for Example 1 evaluated using different tridiagonal
matrices with size n.
PT-symmetric N-by-N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime," Journal of PhysicsA: Mathematical and Theoretical, vol.
Similarly, the vectors [[psi].sup.(od).sub.m] (j), j = 1, ..., M, are the eigenstates of the tridiagonal
M x M matrix [H.sup.(od)]:
Zhang, "Stability of nonlinear systems with tridiagonal
structure and its applications," Acta Automatica Sinica, vol.
The solution in the (n + 1)th time step is obtained by solving the below block tridiagonal
(34) using centered differences for the differential operator and a quadrature formula for the integral operator produces a dense matrix rather than a tridiagonal
matrix, but this problem is still amenable to solution with a conventional eigensolver.
(v) The authors  achieved the values of derivative parameters by solving the three systems of linear equations, which is computationally expensive as compared to methods developed in this paper where there exists only one tridiagonal
system of linear equations for finding the values of derivative parameters.
Further, V[N x N] and H[N x N] are the tridiagonal
matrices obtained from [V.sub.i] and [h.sub.i] elements by using rules defined in .
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.