We have implemented the Bernoulli generic programming system for sparse matrix computations. What distinguishes it from existing generic sparse matrix libraries is that we use (i) a high-level matrix abstraction for writing generic matrix programs, (ii) a low-level matrix abstraction for describing the indexing structure and properties of sparse matrices formats, and (iii) restructuring compile...

An interactive and color graphical front-end package to assist in the study of sparse matrix/vector methods is presented in this paper. The package is written in C and can be installed on any 286 Pc machixie It is designed using an open software architecture. With this package, students can study the sparse matrix/vector methods in a portable and highly user friendly environment. A description ...

. In this paper, we address the dense-sparse matrix product (DSMP) problem i.e. where the first matrix is dense and the second is sparse. We first present initial versions of loop nest structured algorithms corresponding to the most used sparse matrix storing formats i.e. DNS, CSR, CSC and COO. Afterwards, we derive several versions obtained by applying loop interchange techniques, loop invaria...

Hybrid GPU/CPU clusters are becoming very popular in the scientific computing community, as attested by the number of such systems present in the Top 500 list. In this paper, we address one of the key algorithms for scientific applications: the computation of sparse matrix-vector products that lies at the heart of iterative solvers for sparse linear systems. We detail how design patterns for sp...

We discuss issues related to domain decomposition and multilevel preconditioning techniques which are often employed for solving large sparse linear systems in parallel computations. We introduce a class of parallel preconditioning techniques for general sparse linear systems based on a two level block ILU factorization strategy. We give some new data structures and strategies to construct loca...

In this article, we propose a method to perform linear algebra on a matrix with nearly sparse properties. More precisely, although we require the main part of the matrix to be sparse, we allow some dense columns with possibly large coefficients. We modify Block Wiedemann algorithm and show that the contribution of these heavy columns can be made negligible compared to the one of the sparse part...

Cache oblivious algorithms are designed to benefit from any existing cache hierarchy—regardless of cache size or architecture. In matrix computations, cache oblivious approaches are usually obtained from block-recursive approaches. In this article, we extend an existing cache oblivious approach for matrix operations, which is based on Peano space-filling curves, for multiplication of sparse and...

This paper describes Householder reduction of a rectangular sparse matrix to small band upper triangular form. Using block Householder transformations gives good orthogonality, is computationally efficient, and has good potential for parallelization. The algorithm is similar to the standard dense Householder reduction used as part of the usual dense SVD computation. For the sparse algorithm, th...

A sparse matrix multiplication scheme with multiatom blocks is reported, a tool that can be very useful for developing linear-scaling methods with atom-centered basis functions. Compared to conventional element-by-element sparse matrix multiplication schemes, efficiency is gained by the use of the highly optimized basic linear algebra subroutines (BLAS). However, some sparsity is lost in the mu...