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ACM Transactions on Mathematical Software (TOMS), Volume 27 Issue 3, September 2001

A BVP solver based on residual control and the Maltab PSE
Jacek Kierzenka, Lawrence F. Shampine
Pages: 299-316
DOI: 10.1145/502800.502801
Our goal was to make it as easy as possible to solve a large class of boundary value problems (BVPs) for ordinary differential equations in the Matlab problem solving environment (PSE). We present here theoretical and software developments resulting...

Compression of particle data from hierarchical approximate methods
Dow-Yung Yang, Ananth Grama, Vivek Sarin, Naren Ramakrishnan
Pages: 317-339
DOI: 10.1145/502800.502802
This article presents an analytical and computational framework for the compression of particle data resulting from hierarchical approximate treecodes such as the Barnes--Hut and Fast Multipole Methods. Due to approximations introduced...

Algorithm 813: SPG—Software for Convex-Constrained Optimization
Ernesto G. Birgin, José Mario Martínez, Marcos Raydan
Pages: 340-349
DOI: 10.1145/502800.502803
Fortran 77 software implementing the SPG method is introduced. SPG is a nonmonotone projected gradient algorithm for solving large-scale convex-constrained optimization problems. It combines the classical projected gradient method with the spectral...

A revised simplex method with integer Q-matrices
David-Olivier Azulay, Jean-François Pique
Pages: 350-360
DOI: 10.1145/502800.502804
We describe a modification of the simplex formulas in which Q-matrices are used to implement exact computations with an integer multiprecision library. Our motivation comes from the need for efficient and exact incremental solvers in the...

A case study in the performance and scalability of optimization algorithms
Steven J. Benson, Lois Curfman McInnes, Jorge J. Moré
Pages: 361-376
DOI: 10.1145/502800.502805
We analyze the performance and scalabilty of algorithms for the solution of large optimization problems on high-performance parallel architectures. Our case study uses the GPCG (gradient projection, conjugate gradient) algorithm for solving...