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ACM Transactions on Mathematical Software (TOMS), Volume 38 Issue 4, August 2012

Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003
Salvatore Filippone, Alfredo Buttari
Article No.: 23
DOI: 10.1145/2331130.2331131

The efficiency of a sparse linear algebra operation heavily relies on the ability of the sparse matrix storage format to exploit the computing power of the underlying hardware. Since no format is universally better than the others across all...

An Empirical Analysis of the Performance of Preconditioners for SPD Systems
Thomas George, Anshul Gupta, Vivek Sarin
Article No.: 24
DOI: 10.1145/2331130.2331132

Preconditioned iterative solvers have the potential to solve very large sparse linear systems with a fraction of the memory used by direct methods. However, the effectiveness and performance of most preconditioners is not only problem dependent,...

A Runtime System for Programming Out-of-Core Matrix Algorithms-by-Tiles on Multithreaded Architectures
Gregorio Quintana-Ortí, Francisco D. Igual, Mercedes Marqués, Enrique S. Quintana-Ortí, Robert A. van de Geijn
Article No.: 25
DOI: 10.1145/2331130.2331133

Out-of-core implementations of algorithms for dense matrix computations have traditionally focused on optimal use of memory so as to minimize I/O, often trading programmability for performance. In this article we show how the current state of...

Automatic Fréchet Differentiation for the Numerical Solution of Boundary-Value Problems
Asgeir Birkisson, Tobin A. Driscoll
Article No.: 26
DOI: 10.1145/2331130.2331134

A new solver for nonlinear boundary-value problems (BVPs) in Matlab is presented, based on the Chebfun software system for representing functions and operators automatically as numerical objects. The solver implements Newton’s...

Algorithm 920: SFSDP: A Sparse Version of Full Semidefinite Programming Relaxation for Sensor Network Localization Problems
Sunyoung Kim, Masakazu Kojima, Hayato Waki, Makato Yamashita
Article No.: 27
DOI: 10.1145/2331130.2331135

SFSDP is a Matlab package for solving sensor network localization (SNL) problems. These types of problems arise in monitoring and controlling applications using wireless sensor networks. SFSDP implements the semidefinite programming (SDP)...

Algorithm 921: alphaCertified: Certifying Solutions to Polynomial Systems
Jonathan D. Hauenstein, Frank Sottile
Article No.: 28
DOI: 10.1145/2331130.2331136

Smale’s α-theory uses estimates related to the convergence of Newton’s method to certify that Newton iterations will converge quadratically to solutions to a square polynomial system. The program alphaCertified...

Algorithm 922: A Mixed Finite Element Method for Helmholtz Transmission Eigenvalues
Xia Ji, Jiguang Sun, Tiara Turner
Article No.: 29
DOI: 10.1145/2331130.2331137

Transmission eigenvalue problem has important applications in inverse scattering. Since the problem is non-self-adjoint, the computation of transmission eigenvalues needs special treatment. Based on a fourth-order reformulation of the transmission...

Algorithm 923: Efficient Numerical Computation of the Pfaffian for Dense and Banded Skew-Symmetric Matrices
M. Wimmer
Article No.: 30
DOI: 10.1145/2331130.2331138

Computing the Pfaffian of a skew-symmetric matrix is a problem that arises in various fields of physics. Both computing the Pfaffian and a related problem, computing the canonical form of a skew-symmetric matrix under unitary congruence, can be...