In this paper, we develop three essential ingredients of an algebraic structure theory of nite block Hankel matrices. The development centers around a transformation of block Hankel matrices, rst introduced by Fischer and Frobenius for scalar Hankel matrices. We prove three results: First, Iohvidov's fundamental notion of the characteristic of a Hankel matrix is extended to the block matrix cas...

The Lanczos algorithm has proven itself to be a valuable matrix eigensolver for problems with large dimensions, up hundreds of millions or even tens billions. computational cost using any is dominated by the number sparse matrix-vector multiplications required reach suitable convergence. Block replaces multiplication matrix-matrix multiplication; multplication more efficient, due improved data ...

A method for finding the optimal control of singular system with a quadratic cost functional using block pulse function is discussed. After introducing block pulse function in the beginning we develop an operational matrix for solving singular state equations. A numerical example is included to demonstrate the validity and applicability of the technique. Keywords— Optimal control, Singular syst...

Interpolation has wide application in signal processing, numerical integration, Computer Aided Geometric Design (CAGD), engineering technology and electrochemistry. Block based bivariate Newton-like blending rational interpolation can also be calculated based on information matrix algorithm in addition to block divided differences. The paper studied interpolation theorem, dual interpolation of ...

We present some results on almost maximum distance separable (AMDS) codes and Griesmer codes of dimension 4 over F5. We prove that no AMDS code of length 13 and minimum distance 5 exists, and we give a classification of some AMDS codes. Moreover, we classify the projective strongly optimal Griesmer codes over F5 of dimension 4 for some values of the minimum distance.

This paper studies convergence properties of the block GMRES algorithm when applied to nonsymmetric systems with multiple right-hand sides. A convergence theory is developed based on a representation of the method using matrix-valued polynomials. Relations between the roots of the residual polynomial for block GMHES and the matrix &-pseudospectrum are derived, and illustrated with numerical exp...

We consider a special type of signal restoration problem where some of the sampling data are not available. The formulation related to samples of the function and its derivative leads to a possibly large linear system associated to a nonsymmetric block Toeplitz matrix which can be equipped with a 2 × 2 matrix-valued symbol. The aim of the paper is to study the eigenvalues of the matrix. We firs...

We present a new matrix-valued isospectral ordinary differential equation that asymptotically block-diagonalizes n × n zero-diagonal Jacobi matrices employed as its initial condition. This o.d.e. features a right-hand side with a nested commutator of matrices, and structurally resembles the double-bracket o.d.e. studied by R.W. Brockett in 1991. We prove that its solutions converge asymptotical...

This paper studies convergence properties of the block gmres algorithm when applied to nonsymmetric systems with multiple right-hand sides. A convergence theory is developed based on a representation of the method using matrix-valued polynomials. Relations between the roots of the residual polynomial for block gmres and the matrix "-pseudospectrum are derived, and illustrated with numerical exp...

Abstract. This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis. The eigenvalues of the transfer matrix describe localization of eigenstates and are linked to the spectrum of the block tridiagonal matrix by a determinantal identity. If the bl...