The linear system of equations with dense coefficient matrix is very common in science and engineering. In this paper, a parallel algorithm based on Gram-Schmidt QR factorization method for the exact solution of dense system of linear equations is presented. Although several parallel approaches

of rational solutions of square nonsingular systems using adic lifting. The bit complexity of the latter problem is improved by incorporating fast arithmetic and fast matrix multiplication. The resulting randomized algorithm for certified dense linear system solving has substantially better asymptotic

It appears that large scale calculations in particle physics often require to solve systems of linear equations with rational number coefficients exactly. If classical Gaussian elimination is applied to a dense system, the time needed to solve such a system grows exponentially in the size

Two sparse preconditioned iterative methods are presented to solve dense linear systems arising in the solution of two dimensional boundary integral equations. In the first method, the sparse preconditioner is constructed simply by choosing a small block of elements in the coefficient matrix of a

Integral equation methods have been used with great success in electromagnetic scattering calculations and in other problems involving unbounded computational domains. Their application is in many cases limited by the storage requirements of dense matrices and also by the rapidly increasing

In the March 24, 1991 issue of NA Digest, I submitted a questionnaire asking who was solving large dense linear systems of equations. Based on the responses, nearly all large dense linear systems today arise from either the benchmarking of supercomputers or applications involving the influence of a

We present several algorithms to compute the solution of a linear system of equa-tions on a GPU, as well as general techniques to improve their performance, such as padding and hybrid GPU-CPU computation. We also show how iterative refinement with mixed-precision can be used to regain full accuracy

. We investigate the use of sparse approximate inverse preconditioners for the iterative solution of linear systems with dense complex coefficient matrices arising from industrial electromagnetic problems. An approximate inverse is computed via a Frobenius norm approach with a prescribed nonzero

We present a novel algorithm to solve dense linear systems using graphics processors (GPUs). We reduce matrix decomposition and row operations to a series of rasterization problems on the GPU. These include new techniques for streaming index pairs, swapping rows and columns and parallelizing

The most efficient previously known parallel algorithms for the inversion of a nonsingular n x n matrix .4 or solving a linear system/Ix = b over the rational numbers require O(logn) time and M(n).x/ processors [provided that M(n) processors suffice in order to multiply two n x n rational