The application of the conjugate gradient (CG) algorithm to the problem of data reconstruction in SPECT imaging indicates that most of the useful information is already contained in Krylov subspaces of small dimension, ranging from 9 (two-dimensional case) to 15 (three-dimensional case). On this basis, a new, proposed approach can be basically summarized as follows: construction of a basis span...

In this paper we deal with performance analysis of Monte Carlo algorithm for large linear algebra problems. We consider applicability and efficiency of the Markov chain Monte Carlo for large problems, i.e., problems involving matrices with a number of non-zero elements ranging between one million and one billion. We are concentrating on analysis of the almost Optimal Monte Carlo (MAO) algorithm...

We present an extension of the framework of Gaul et al. (SIAM J. Matrix Anal. Appl. 34, 495–518 (2013)) for deflated and augmented Krylov subspace methods satisfying a Galerkin condition to more general Petrov–Galerkin conditions. The main goal is to apply the framework to the biconjugate gradient method (BiCG) and some of its generalizations, including BiCGStab and IDR(s). For such application...

s 6 Awad H. Al-Mohy An Improved Algorithm for the Matrix Logarithm . . . . . . . . . . . . . . . . . . . . 7 David Amsallem Interpolation on Matrix Manifolds of Reduced-Order Models and Application to On-Line Aeroelastic Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Athanasios C. Antoulas Model Reduction of Parameter-Dependent Systems . . . . . . . . . . . . . . . . . . ...

The performance of Krylov subspace eigenvalue algorithms for large matrices can be measured by the angle between a desired invariant subspace and the Krylov subspace. We develop general bounds for this convergence that include the effects of polynomial restarting and impose no restrictions concerning the diagonalizability of the matrix or its degree of nonnormality. Associated with a desired se...

Model reduction techniques are needed to directly solve the chemical master equation (CME) due to its enormous size. We recently described an algorithm that solved the CME by combining the finite state projection, stochastic simulation algorithm and Krylov subspace approximations. In this work, we add further improvements that consist of an incomplete orthogonalization process with Krylov subsp...