embedded orthogonal transition matrix to the a-ertended upper Hessenberg form, and (iii) factorization of this new form into Givens (planar) rotations. Appropriately interconnecting the rotors leads to the pipelined orthogonal filter structure. As a consequence of our approach, for the SISO case, an essentially orthogonal structure is obtained for the inverse filter; only one of the Givens roto...

T h e B R algorithm, a new method for calculating the eigenvalues of an upper Hessenberg matrix, is introduced. I t is a bulge-chasingalgorithm like the Q R algorithm, but , unlike the QR algorithm, it is well adapted to computing the eigenvaluesof the narrow-band, nearly tridiagonal matrices generated by the look-ahead Lanczos process. This paper describes the B R algorithm and gives numerical...

In this paper we discuss matrix decompositions in the symmetrized max-plus algebra. The max-plus algebra has maximization and addition as basic operations. In contrast to linear algebra many fundamental problems in the max-plus algebra still have to be solved. In this paper we discuss max-algebraic analogues of some basic matrix decompositions from linear algebra. We show that we can use algori...

In this paper we describe block algorithms for the reduction of a real symmetric matrix to tridiagonal form and for the reduction of a general real matrix to either bidiagonal or Hessenberg form using Householder transformations. The approach is to aggregate the transformations and to apply them in a blocked fashion, thus achieving algorithms that are rich in matrix-matrix operations. These red...

In this paper we describe block algorithms for the reduction of a real symmetric matrix to tridiagonal form and for the reduction of a general real matrix to either bidiagonal or Hessenberg form using Householder transformations. The approach is to aggregate the transformations and to apply them in a blocked fashion, thus achieving algorithms that are rich in matrix-matrix operations. These red...

In this paper we describe block algorithms for the reduction of a real symmetric matrix to tridiagonal form and for the reduction of a general real matrix to either bidiagonal or Hessenberg form using Householder transformations. The approach is to aggregate the transformations and to apply them in a blocked fashion, thus achieving algorithms that are rich in matrix-matrix operations. These red...

We consider k sequences of generalized order-k linear recurrences with arbitrary initial conditions and coefficients, and we give their generalized Binet formulas and generating functions. We also obtain a new matrix method to derive explicit formulas for the sums of terms of the k sequences. Further, some relationships between determinants of certain Hessenberg matrices and the terms of these ...

Recently, a spectral Favard theorem was presented for bounded banded lower Hessenberg matrices that possess positive bidiagonal factorization. The paper establishes conditions, expressed in terms of continued fractions, under which an oscillatory tetradiagonal matrix can have such Oscillatory Toeplitz are examined as case study admit Furthermore, the proves organized rays, where origin ray does...

There are many classical results in which orthogonal vectors stemming from Krylov subspaces are linked to short recurrence relations, e.g., three-terms recurrences for Hermitian and short rational recurrences for unitary matrices. These recurrence coefficients can be captured in a Hessenberg matrix, whose structure reflects the relation between the spectrum of the original matrix and the recurr...

In this paper we discuss matrix decompositions in the symmetrized max-plus algebra. The max-plus algebra has maximization and addition as basic operations. In contrast to linear algebra many fundamental problems in the max-plus algebra still have to be solved. In this paper we discuss max-algebraic analogues of some basic matrix decompositions from linear algebra. We show that we can use algori...