In this paper, we consider using Galerkin projection methods for solving multiple linear systems A (i) x (i) = b (i) , for 1 i s, where the coeecient matrices A (i) and the right-hand sides b (i) are diierent in general. In particular, we focus on the seed projection method which generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed ...

A deflated restarted Lanczos algorithm is given for both solving symmetric linear equations and computing eigenvalues and eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Meanwhile, the deflating from the presence of the eigenvectors allows the linear equations to generally have good convergence in spite of the restarting. Some reorthogonalization is ne...

This paper is concerned with solving large scale linear fractional multiple objective programming (LSLFMOP) problems with chance constraints. Channce constraints involve random parameters in the right-hand sides. These random right-hand sides are considered to be statistically independent random variable. The main features of the proposed solution procedure are based on chanceconstrained techni...

I will review recent developments in matrix deflation methods, by Ronald Morgan/Walter Wilcox, Andreas Stathopoulos/Konstantinos Orginos, and Martin Lüscher, with application to lattice QCD fermion inversion. I will begin with a short review of deflation-related work in the field. The Morgan/Wilcox algorithms using GMRES and BiCGStab for deflation will be described. Typical results for quenched...

Many applications require the solution of large nonsymmetric linear systems with multiple right-hand sides. Instead of applying an iterative method to each of these systems individually, it is often more eecient to use a block version of the method that generates iterates for all the systems simultaneously. In this paper, we propose block versions of Galerkin/minimal residual pair of bidiagonal...

With the development of the VLSI circuits, the feature size has been decreased to the deep sub-micron level, and the working frequency has reached to 3GHz. In order to assure the correctness of the IC design with high performance, the parasitic interconnect inductance and resistance should he calculated quickly and accurately. In this paper, the multipole method with modified non-uniform cube p...

Recently, the complementary behavior of restarted GMRES has been studied. We observed that successive cycles of restarted block BGMRES (BGMRES(m,s)) can also complement one another harmoniously in reducing the iterative residual. In the present paper, this characterization of BGMRES(m,s) is exploited to form a hybrid block iterative scheme. In particular, a product hybrid block GMRES algorithm ...