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ACM Transactions on Mathematical Software (TOMS), Volume 35 Issue 1, July 2008

Hybrid differentiation strategies for simulation and analysis of applications in C++
Roscoe A. Bartlett, Bart G. Van Bloemen Waanders, Martin Berggren
Article No.: 1
DOI: 10.1145/1377603.1377604

Computationally efficient and accurate derivatives are important to the success of many different types of numerical methods. Automatic differentation (AD) approaches compute truncation-free derivatives and can be efficient in many cases. Although...

Optimal vertex elimination in single-expression-use graphs
Uwe Naumann, Yuxiao Hu
Article No.: 2
DOI: 10.1145/1377603.1377605

The source transformation tool for automatic differentiation of Fortran programs ADIFOR uses a preaccumulation technique to speed up tangent-linear codes significantly compared to the standard forward mode. Reverse mode automatic differentiation...

Families of algorithms related to the inversion of a Symmetric Positive Definite matrix
Paolo Bientinesi, Brian Gunter, Robert A. van de Geijn
Article No.: 3
DOI: 10.1145/1377603.1377606

We study the high-performance implementation of the inversion of a Symmetric Positive Definite (SPD) matrix on architectures ranging from sequential processors to Symmetric MultiProcessors to distributed memory parallel computers. This inversion...

High-performance implementation of the level-3 BLAS
Kazushige Goto, Robert Van De Geijn
Article No.: 4
DOI: 10.1145/1377603.1377607

A simple but highly effective approach for transforming high-performance implementations on cache-based architectures of matrix-matrix multiplication into implementations of other commonly used matrix-matrix computations (the level-3 BLAS) is...

Evaluating exact VARMA likelihood and its gradient when data are incomplete
Kristjan Jonasson, Sebastian E. Ferrando
Article No.: 5
DOI: 10.1145/1377603.1377608

A detailed description of an algorithm for the evaluation and differentiation of the likelihood function for VARMA processes in the general case of missing values is presented. The method is based on combining the Cholesky decomposition method for...

Algorithm 878: Exact VARMA likelihood and its gradient for complete and incomplete data with Matlab
Kristjan Jonasson
Article No.: 6
DOI: 10.1145/1377603.1377609

Matlab functions for the evaluation of the exact log-likelihood of VAR and VARMA time series models are presented (vector autoregressive moving average). The functions accept incomplete data, and calculate analytical gradients, which may be used...

Algorithm 879: EIGENTEST—a test matrix generator for large-scale eigenproblems
Che-Rung Lee, G. W. Stewart
Article No.: 7
DOI: 10.1145/1377603.1377610

Eigentest is a package that produces real test matrices with known eigensystems. A test matrix, called an eigenmat, is generated in a factored form, in which the user can specify the eigenvalues and has some control over the condition of the...

Algorithm 880: A testing infrastructure for symmetric tridiagonal eigensolvers
Osni A. Marques, Christof Vömel, James W. Demmel, Beresford N. Parlett
Article No.: 8
DOI: 10.1145/1377603.1377611

LAPACK is often mentioned as a positive example of a software library that encapsulates complex, robust, and widely used numerical algorithms for a wide range of applications. At installation time, the user has the option of running a (limited)...