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ACM Transactions on Mathematical Software (TOMS), Volume 36 Issue 2, March 2009

A software framework for abstract expression of coordinate-free linear algebra and optimization algorithms
Anthony D. Padula, Shannon D. Scott, William W. Symes
Article No.: 8
DOI: 10.1145/1499096.1499097

The Rice Vector Library is a collection of C++ classes expressing core concepts (vector, function,…) of calculus in Hilbert space with minimal implementation dependence, and providing standardized interfaces behind which to hide...

An out-of-core sparse Cholesky solver
John K. Reid, Jennifer A. Scott
Article No.: 9
DOI: 10.1145/1499096.1499098

Direct methods for solving large sparse linear systems of equations are popular because of their generality and robustness. Their main weakness is that the memory they require usually increases rapidly with problem size. We discuss the design and...

KSSOLV—a MATLAB toolbox for solving the Kohn-Sham equations
Chao Yang, Juan C. Meza, Byounghak Lee, Lin-Wang Wang
Article No.: 10
DOI: 10.1145/1499096.1499099

We describe the design and implementation of KSSOLV, a MATLAB toolbox for solving a class of nonlinear eigenvalue problems known as the Kohn-Sham equations. These types of problems arise in electronic structure calculations, which are...

Distributed SBP Cholesky factorization algorithms with near-optimal scheduling
Fred G. Gustavson, Lars Karlsson, Bo Kågström
Article No.: 11
DOI: 10.1145/1499096.1499100

The minimal block storage Distributed Square Block Packed (DSBP) format for distributed memory computing on symmetric and triangular matrices is presented. Three algorithm variants (Basic, Static, and Dynamic) of the blocked right-looking Cholesky...

Algorithm 894: On a block Schur--Parlett algorithm for ϕ-functions based on the sep-inverse estimate
Souji Koikari
Article No.: 12
DOI: 10.1145/1499096.1499101

FORTRAN 95 software is provided for computing the matrix values of ϕ-functions required in exponential integrators. The subroutines in the library accept as their argument a full, diagonal, or upper quasitriangular matrix with real or complex...