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We discuss the design, implementation, and benchmarking of a system that can manipulate symbolic expressions represented by their straight-line computations. Our system is capable of performing rational arithmetic on, evaluating, differentiating, taking greatest common divisors of, and factoring...
This paper describes some simple programming language facilities for raising and handling exceptions, and demonstrates, with a number of examples, their effectiveness in a scientific computing environment. Only a small number of predefined exceptions need to be introduced into the language, but...
A FORTRAN 77 implementation of a Gauss algorithm with partial pivoting for banded matrices is described. The algorithm keeps only part of the matrix that is necessary for the actual computation in memory. This allows large systems to be solved on machine without virtual memory, or if the virtual...
An algorithm to generate variates having a gamma distribution with shape parameter greater than one is presented in this paper. This algorithm is faster than Schmeiser and Lal's G4PE, which is the fastest one currently available, yet is equally simple and easy to implement.
This paper describes a new implementation of algorithms for solving large, dense symmetric eigen-problems AX = BX ण, where the matrices A and B are too large to fit in the central memory of the computer. Here A is assumed to be symmetric, and B symmetric positive definite. A combination of...
We examine an implementation and a number of modifications of a 1973 algorithm of Hopcroft and Karp for permuting a sparse matrix so that there are no zeros on the diagonal. We describe our implementation of the original Hopcroft and Karp algorithm and compare this with modifications which we...
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