Suppose that one knows an accurate approximation to an eigenvalue of a real symmetric tridiagonal matrix. A variant of deflation by the Givens rotations is proposed in order to split off the approximated eigenvalue. Such a deflation can be used instead of inverse iteration to compute the corresponding eigenvector. © 2002 Elsevier Science Inc. All rights reserved.

Previously, we have discussed a recursive solution to the vector normal equation utilizing the recursive Cholesky and Modified Gram-Schmidt Orthogonalization (MGSO) algorithms. Previously, we have also discussed a blind adaptive approach for detection and extraction of signals of interest in the presence of noise and interference without relying on preamble or training sequences. The heart of t...

We present two efficient iterative algorithms for solving the linear response eigenvalue problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into a product ...

This paper takes another look at the convergence of the Arnoldi procedure forsolving nonsymmetric eigenvalue problems. Three different viewpoints are considered. The first usesa bound on the distance from the eigenvector to the Krylov subspace from the smallest singularvalue of matrix consisting of the Krylov basis. A second approach relies on the Schur factorization.Finally, a ...

Presented are two related numerical methods, one for the inverse eigenvalue problem for nonnegative or stochastic matrices and another for the inverse eigenvalue problem for symmetric nonnegative matrices. The methods are iterative in nature and utilize alternating projection ideas. For the symmetric problem, the main computational component of each iteration is an eigenvalue-eigenvector decomp...

RNA secondary structure consists of elements such as stems, bulges, loops. The most obvious and important scalar number that can be attached to an RNA structure is its free energy, with a landscape that governs the folding pathway. However, because of the unique geometry of RNA secondary structure, another interesting single-signed scalar number based on geometrical scales exists that can assis...

We address the problem of computing the largest fraction of missing information for the EM algorithm and the worst linear function for data augmentation These are the largest eigenvalue and its associated eigenvector for the Jacobian of the EM operator at a maximum likelihood estimate which are important for assessing convergence in iterative simulation An estimate of the largest fraction of mi...

in this paper, we present an edge detection method based on wavelet transform and hessian matrix of image at each pixel. many methods which based on wavelet transform, use wavelet transform to approximate the gradient of image and detect edges by searching the modulus maximum of gradient vectors. in our scheme, we use wavelet transform to approximate hessian matrix of image at each pixel, too. ...