In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas p-polynomials, ordinary Lucas and Perrin sequences etc., by using various Hessenberg matrices. In addition, we show that determinant and permanent of these Hessenberg matrices can be obtained by using combinations. Then we show, the ...

In this paper‎, ‎we define two $n$-square upper Hessenberg matrices one of which corresponds to the adjacency matrix of a directed pseudo graph‎. ‎We investigate relations between permanents and determinants of these upper Hessenberg matrices‎, ‎and sum formulas of the well-known Pell and Jacobsthal sequences‎. ‎Finally‎, ‎we present two Maple 13 procedures in order to calculate permanents of t...

in this paper‎, ‎we define two $n$-square upper hessenberg matrices one of which corresponds to the adjacency matrix of a directed pseudo graph‎. ‎we investigate relations between permanents and determinants of these upper hessenberg matrices‎, ‎and sum formulas of the well-known pell and jacobsthal sequences‎. ‎finally‎, ‎we present two maple 13 procedures in order to calculate permanents of t...

is a Hessenberg matrix and its determinant is F2n+2. Furthermore, a Hessenberg matrix is said to be a Fibonacci-Hessenberg matrix [2] if its determinant is in the form tFn−1 + Fn−2 or Fn−1 + tFn−2 for some real or complex number t. In [1] several types of Hessenberg matrices whose determinants are Fibonacci numbers were calculated by using the basic definition of the determinant as a signed sum...

in this paper, we give some determinantal and permanental representations of generalized lucas polynomials, which are a general form of generalized bivariate lucas p-polynomials, ordinary lucas and perrin sequences etc., by using various hessenberg matrices. in addition, we show that determinant and permanent of these hessenberg matrices can be obtained by using combinations. then we show, the ...

A new proof of the general representation for the entries of the inverse of any unreduced Hessenberg matrix of finite order is found. Also this formulation is extended to the inverses of reduced Hessenberg matrices. Those entries are given with proper Hessenbergians from the original matrix. It justifies both the use of linear recurrences for such computations and some elementary properties of ...

The design, implementation and performance of a parallel algorithm for reduction of a matrix pair in block upper Hessenberg-Triangular form (Hr, T ) to upper Hessenberg-triangular form (H, T ) is presented. This reduction is the second stage in a two-stage reduction of a regular matrix pair (A, B) to upper Hessenberg-Triangular from. The desired upper Hessenberg-triangular form is computed usin...

The QR-algorithm is a renowned method for computing all eigenvalues of an arbitrary matrix. A preliminary unitary similarity transformation to Hessenberg form is indispensible for keeping the computational complexity of the QRalgorithm applied on the resulting Hessenberg matrix under control. The unitary factor Q in the QR-factorization of the Hessenberg matrix H = QR is composed of n − 1 rotat...

It is well known that the projection of a matrix A onto a Krylov subspace span { h, Ah, Ah, . . . , Ak−1h } results in a matrix of Hessenberg form. We show that the projection of the same matrix A onto an extended Krylov subspace, which is of the form span { A−krh, . . . , A−2h, A−1h,h, Ah, Ah . . . , A`h } , is a matrix of so-called extended Hessenberg form which can be characterized uniquely ...

We introduce in this paper a method to calcúlate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G. Mantica to calcúlate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures. We apply this method to approximate the Hessenberg matrix associated wit...