In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of ...

X iv :m at h/ 05 12 22 2v 1 [ m at h. SP ] 1 1 D ec 2 00 5 The asymptotic properties of the spectrum of non symmetrically perturbed Jacobi matrix sequences Leonid Golinskii and Stefano Serra-Capizzano 1 Abstract Under the mild trace-norm assumptions, we show that the eigenvalues of a generic (non Hermitian) complex perturbation of a Jacobi matrix sequence (not necessarily real) are still distri...

We discuss the notion of Jacobi forms of degree one with matrix index, we state dimension formulas, give explicit examples, and indicate how closely their theory is connected to the theory of invariants of Weil representations associated to finite quadratic modules. 1 Jacobi forms of degree one Jacobi forms of degree one with matrix index F gained recent interest, mainly due to applications in ...

This paper proposes the periodical successive over-relaxation (PSOR)-Jacobi algorithm for minimum mean squared error (MMSE) detection of multiple-input multiple-output (MIMO) signals. The proposed has advantages two conventional methods. One is Jacobi method, which an iterative method solving linear equations and suitable parallel implementation. thus a promising candidate high-speed simultaneo...

Abstract. The discrete spectrum of complex banded matrices that are compact perturbations of the standard banded matrix of order p is under consideration. The rate of stabilization for the matrix entries sharp in the sense of order which provides finiteness of the discrete spectrum is found. The pbanded matrix with the discrete spectrum having exactly p limit points on the interval (−2, 2) is c...

This paper is the result of contrived efforts to break the barrier between numerical accuracy and run time efficiency in computing the fundamental decomposition of numerical linear algebra – the singular value decomposition (SVD) of a general dense matrix. It is an unfortunate fact that the numerically most accurate one–sided Jacobi SVD algorithm is several times slower than generally less accu...

Matrix inversion is routinely performed in computational engineering, with coupling matrix filter synthesis considered here as just one of many example applications. When calculating the elements of the inverse of a matrix, the determinants of the submatrices are evaluated. The recent mathematical proof of the Desnanot–Jacobi (also known as the ‘‘Lewis Carol’’) identity shows how the determinan...