Mathematical Software (TOMS)


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ACM Transactions on Mathematical Software (TOMS), Volume 34 Issue 4, July 2008

Using Mixed Precision for Sparse Matrix Computations to Enhance the Performance while Achieving 64-bit Accuracy
Alfredo Buttari, Jack Dongarra, Jakub Kurzak, Piotr Luszczek, Stanimir Tomov
Article No.: 17
DOI: 10.1145/1377596.1377597

By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. These ideas can be...

OpenAD/F: A Modular Open-Source Tool for Automatic Differentiation of Fortran Codes
Jean Utke, Uwe Naumann, Mike Fagan, Nathan Tallent, Michelle Strout, Patrick Heimbach, Chris Hill, Carl Wunsch
Article No.: 18
DOI: 10.1145/1377596.1377598

The Open/ADF tool allows the evaluation of derivatives of functions defined by a Fortran program. The derivative evaluation is performed by a Fortran code resulting from the analysis and transformation of the original program that defines the...

Efficient Contouring on Unstructured Meshes for Partial Differential Equations
Hassan Goldani-Moghaddam, Wayne H. Enright
Article No.: 19
DOI: 10.1145/1377596.1377599

We introduce three fast contouring algorithms for visualizing the solution of partial differential equations based on the PCI (pure cubic interpolant). The PCI is a particular piecewise bicubic polynomial interpolant defined over an unstructured...

An Implementation and Evaluation of the AMLS Method for Sparse Eigenvalue Problems
Weiguo Gao, Xiaoye S. Li, Chao Yang, Zhaojun Bai
Article No.: 20
DOI: 10.1145/1377596.1377600

We describe an efficient implementation and present a performance study of an automated multi-level substructuring (AMLS) method for sparse eigenvalue problems. We assess the time and memory requirements associated with the key steps of the...

Algorithm 876: Solving Fredholm Integral Equations of the Second Kind in Matlab
Kendall E. Atkinson, Lawrence F. Shampine
Article No.: 21
DOI: 10.1145/1377596.1377601

We present here the algorithms and user interface of a Matlab program, Fie, that solves numerically Fredholm integral equations of the second kind on an interval [a,b] to a specified, modest accuracy. The kernel function...

Algorithm 877: A Subroutine Package for Cylindrical Functions of Complex Order and Nonnegative Argument
Masao Kodama
Article No.: 22
DOI: 10.1145/1377596.1377602

The algorithm presented provides a package of subroutines for calculating the cylindrical functions Jν(x), Nν(x), Hν(1)(x),...