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ACM Transactions on Mathematical Software (TOMS) - The MIT Press scientific computation series, Volume 12 Issue 1, March 1986

Fixed versus variable order Runge-Kutta
L. F. Shampine, L. S. Baca
Pages: 1-23
DOI: 10.1145/5960.5964
Popular codes for the numerical solution of nonstiff ordinary differential equations (ODEs) are based on a (fixed order) Runge-Kutta method, a variable order Adams method, or an extrapolation method. Extrapolation can be viewed as a variable...

Algorithm 639: To integrate some infinite oscillating tails
James Lyness, Gwendolen Hines
Pages: 24-25
DOI: 10.1145/5960.214318

Algorithm 640: Efficient calculation of frequency response matrices from state space models
Alan J. Laub
Pages: 26-33
DOI: 10.1145/5960.214319

The economical method for generating random samples from discrete distributions
I. Deak
Pages: 34-36
DOI: 10.1145/5960.214321
The idea of the economical method is applied for generating samples from any discrete distribution. In the resulting procedure, the expected number of uniformly distributed random numbers is less than in the alias method (practically 1). A...

A node-addition model for symbolic factorization
Kincho H. Law, Steven J. Fenives
Pages: 37-50
DOI: 10.1145/5960.5963
A symbolic node-addition model for matrix factorization of symmetric positive definite matrices is described. In this model, the nodes are added onto the filled graph one at a time. The advantage of the node-addition model is its simplicity and...

Exact solution of general integer systems of linear equations
Jörn Springer
Pages: 51-61
DOI: 10.1145/5960.5961
Methods are known for the exact computation of the solution of integer systems of linear equations AX = B with a nonsingular coefficient matrix A by congruence techniques. These methods are now...

High-accuracy arithmetic software—some tests of the ACRITH problem-solving routines
Paul Jansen, Peter Weidner
Pages: 62-70
DOI: 10.1145/5960.5962
The program package ACRITH (High-Accuracy Arithmetic Subroutine Library) provides FORTRAN subroutines for the solution of several standard mathematical problems. The routines use floating point operations with extended precision and interval...

Remark on “Algorithm 584: CUBTRI: Automatic Cubature over a Triangle”
Richard J. Hanson
Page: 71
DOI: 10.1145/5960.356162

Remark on “Algorithm 631: Finding a Bracketed Zero by Larkin's Method of Rational Interpolation”
Victor Norton
Page: 72
DOI: 10.1145/5960.356163