In this paper, we give some relations involving the usual Fibonacci and generalized order-k Pell numbers. These relations show that the generalized order-k Pell numbers can be expressed as the summation of the usual Fibonacci numbers. We …nd families of Hessenberg matrices such that the permanents of these matrices are the usual Fibonacci numbers, F2i 1; and their sums. Also extending these mat...

In this paper we consider the numerical solution of initial value delay-diierential-algebraic equations (DDAEs) of retarded and neutral types, with a structure corresponding to that of Hessenberg DAEs. We give conditions under which the DDAE is well-conditioned, and show how the DDAE is related to an underlying retarded or neutral delay-ODE (DODE). We present convergence results for linear mult...

Abstract We present some accelerated variants of fixed point iterations for computing the minimal non-negative solution unilateral matrix equation associated with an M/G/1-type Markov chain. These derive from certain staircase regular splittings block Hessenberg M-matrix By exploiting profile, we introduce a two-step iteration. The iteration can be further by weighted average between approximat...

Hessenberg differential algebraic equations (Hessenberg-DAEs) with a high index play critical role in the modeling of mechanical systems and multibody dynamics. Motivated by widely used Lie-group equation (LGDAE) method, which handles index-2 systems, we first propose modified extended (MELGDAE) method for solving index-3 Hessenberg-DAEs then provide theoretical analysis to deepen foundation ME...

Five new classes of Fibonacci-Hessenberg matrices are introduced. Further, we introduce the notion of two-dimensional Fibonacci arrays and show that three classes of previously known Fibonacci-Hessenberg matrices and their generalizations satisfy this property. Simple systems of linear equations are given whose solutions are Fibonacci fractions.

A new approach to the computation of the poles of a stable autoregressive system from the reeection coeecients is proposed. Equivalently, we compute the zeros of Szeg} o polynomials from the associated Schur parameters. The numerical method utilizes an eecient algorithm for computing the (unimodular) zeros of a unitary Hessenberg matrix; this step can be regarded as the computation of the poles...

Abstract. We introduce a spectral transform for the finite relativistice Toda lattice (RTL) in generalized form. In the nonrelativistic case, Moser constructed a spectral transform from the spectral theory of symmetric Jacobi matrices. Here we use a nonsymmetric generalized eigenvalue problem for a pair of bidiagonal matrices (L, M) to define the spectral transform for the RTL. The inverse spec...

It is a well-known fact that while reducing a symmetric matrix into a similar tridiagonal one, the already tridiagonal matrix in the partially reduced matrix has as eigenvalues the Lanczos-Ritz values (see e.g. [Golub G. and Van Loan C.] ). This behavior is also shared by the reduction algorithm which transforms symmetric matrices via orthogonal similarity transformations to semiseparable form ...

We consider the computing issues of steady probabilities for block-structured discrete-time Markov chains that are upper-Hessenberg or lower-Hessenberg transition kernels with a continuous phase set. An effective computational framework is proposed based on wavelet transform, which extends and modifies arguments in literature quasi-birth-death (QBD) processes. A numerical procedure developed fa...