Existing direct solvers for large linear systems, especially sparse ones, require the matrices to be explicitly available. In practical computations, often only matrix-vector products instead of the matrix are available, which makes iterative methods the only choice. Here, we derive matrix-free sparse direct solvers based on matrixvector products. Two stages are involved. The first stage is to ...

Routines callable from FORTRAN and C are described which implement matrix–matrix multiplication and transposition for a variety of sparse matrix formats. Conversion routines between various formats are provided.

Sparse storage formats are techniques for storing and processing the sparse matrix data efficiently. The performance of these storage formats depend upon the distribution of non-zeros, within the matrix in different dimensions. In order to have better results we need a technique that suits best the organization of data in a particular matrix. So the decision of selecting a better technique is t...

Matrices appearing in Hartree–Fock or density functional theory coming from discretization with help of atom–centered local basis sets become sparse when the separation between atoms exceeds some system–dependent threshold value. Efficient implementation of sparse matrix algebra is therefore essential in large–scale quantum calculations. We describe a unique combination of algorithms and data r...

Run-time support for the CYCLIC(k) redistribution on the SPMD computation model is presently very relevant for the scientific community. This work is focused to the characterization of the sparse matrix redistribution and its associate problematic due to the use of compressed representations. Two main improvements about the buffering and the coordinates calculation modify the original algorithm...

Partitioned global address space (PGAS) languages, such as Unified Parallel C (UPC) have the promise of being productive. Due to the shared address space view that they provide, they make distributing data and operating on ghost zones relatively easy. Meanwhile, they provide thread-data affinity that can enable locality exploitation. In this paper, we are considering sparse matrix multiplicatio...