GMRES(k) is widely used for solving nonsymmetric linear systems. However, it is inadequate either when it converges only for k close to the problem size or when numerical error in the modified Gram–Schmidt process used in the GMRES orthogonalization phase dramatically affects the algorithm performance. An adaptive version of GMRES(k) which tunes the restart value k based on criteria estimating ...

We discuss some features of the orthogonalization methods commonly applied to QSPR QSAR studies. We outline the well known multivariable linear regression analysis in vector form in order to compare mainly Randic and Gram-Schmidt orthogonalization procedures and also cast the basis for other approaches like Löwdin’s one. We expect that present review may become the starting point for future dev...

In this paper, we compare with the inverse iteration algorithms on PowerXCell 8i processor, which has been known as a heterogeneous environment. When some of all the eigenvalues are close together or there are clusters of eigenvalues, reorthogonalization must be adopted to all the eigenvectors associated with such eigenvalues. Reorthogonalization algorithms need a lot of computational cost. The...

Convergence acceleration by preconditioning is usually essential when solving the standard least squares problems by an iterative method. IMGS, is an incomplete modiied version of Gram-Schmidt orthogonalization to obtain an incomplete orthogonal factorization pre-conditioner M = R, where A = Q R + E is an approximation of a QR factorization, Q is an orthogonal matrix and R is upper triangular m...

This report presents a faster version of the polynomial recursive orthogonalization (PRO) algorithm, which is used in segmented image coding to generate orthonormal base functions on a non-rectangular discrete image. It shows that up to 25% of the oating point operations can be eliminated by using previously computed results; also, some orthogonalizations can be avoided altogether, because they...