Block BiCGGR: a new Block Krylov subspace method for computing high accuracy solutions

A New Block Krylov Subspace Method for Computing High Accuracy Solutions

In this paper, the influence of errors which arise in matrix multiplications on the accuracy of approximate solutions generated by the Block BiCGSTAB method is analyzed. In order to generate high accuracy solutions, a new Block Krylov subspace method is also proposed. Some numerical experiments illustrate that high accuracy solutions can be obtained by using the proposed method compared with th...

Block Krylov Subspace Spectral Methods for Variable-Coefficient Elliptic PDE

Krylov subspace spectral (KSS) methods have been demonstrated to be effective tools for solving time-dependent variable-coefficient PDE. They employ techniques developed by Golub and Meurant for computing elements of functions of matrices to approximate each Fourier coefficient of the solution using a Gaussian quadrature rule that is tailored to that coefficient. In this paper, we apply this sa...

A block inverse-free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems

Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions

In many data-intensive applications, the use of principal component analysis (PCA) and other related techniques is ubiquitous for dimension reduction, data mining or other transformational purposes. Such transformations often require efficiently, reliably and accurately computing dominant singular value decompositions (SVDs) of large unstructured matrices. In this paper, we propose and study a ...

A block Krylov subspace time-exact solution method for linear ordinary differential equation systems

We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form y D Ay C g.t/ and y D Ay C g.t/, where y.t/ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of the source term g.t/, constructed with the help of the truncated singular value decomposition. The se...