ACM Transactions on Mathematical Software (TOMS)

van Snyder, W.

doi: 10.1145/168173.168193pmid: N/A

An implementation of approximations for Fresnel integrals and associated functions is described. The approximations were originally developed by W. J. Cody, but a Fortran implementation using them has not previously been published.

van Snyder, W.

doi: 10.1145/168173.168193pmid: N/A

An implementation of approximations for Fresnel integrals and associated functions is described. The approximations were originally developed by W. J. Cody, but a Fortran implementation using them has not previously been published.

Ribbens, Calvin J.; Watson, Layne T.; Desa, Colin

doi: 10.1145/168173.168383pmid: N/A

Three approaches to parallelizing important components of the mathematical software package ELLPACK are considered: an explicit approach using compiler directives available only on the target machine, an automatic approach using an optimizing and parallelizing precompiler, and a two-level approach based on extensive use of a set of low level computational kernels. The focus is on shared memory architectures. Each approach to parallelization is described in detail, along with a discussion of the effort involved. Performance on a test problem, using up to sixteen processors of a Sequent Symmetry S81, is reported and discussed. Implications for the parallelization of a broad class of mathematical software are drawn.

Ribbens, Calvin J.; Watson, Layne T.; Desa, Colin

doi: 10.1145/168173.168383pmid: N/A

Three approaches to parallelizing important components of the mathematical software package ELLPACK are considered: an explicit approach using compiler directives available only on the target machine, an automatic approach using an optimizing and parallelizing precompiler, and a two-level approach based on extensive use of a set of low level computational kernels. The focus is on shared memory architectures. Each approach to parallelization is described in detail, along with a discussion of the effort involved. Performance on a test problem, using up to sixteen processors of a Sequent Symmetry S81, is reported and discussed. Implications for the parallelization of a broad class of mathematical software are drawn.

Abernathy, Roger W.; Smith, Robert P.

doi: 10.1145/168173.168387pmid: N/A

Let 0 ≤ 1 and F be the cumulative distribution function (cdf) of the F -Distribution. We wish to find x p such that F(x p |n 1 , n 2 ) = p , where n 1 and n 2 are the degrees of freedom. Traditionally, x p is found using a numerical root-finding method, such as Newton's method. In this paper, a procedure based on a series expansion for finding x p is given. The series expansion method has been applied to the normal, chi-square, and t distributions, but because of computational difficulties, it has not been applied to the F -Distribution. These problems have been overcome by making the standard transformation to the beta distribution. The procedure is explained in Sections 3 and 4. Empirical results of a comparison of CPU times are given in Section 5. The series expansion is compared to some of the standard root-finding methods. A table is given for p = .90.

Abernathy, Roger W.; Smith, Robert P.

doi: 10.1145/168173.168387pmid: N/A

Let 0 1 and F be the cumulative distribution function (cdf) of the F-Distribution. We wish to find xp such that F(xp|n1, n2) = p, where n1 and n2 are the degrees of freedom. Traditionally, xp is found using a numerical root-finding method, such as Newton's method. In this paper, a procedure based on a series expansion for finding xpis given. The series expansion method has been applied to the normal, chi-square, and t distributions, but because of computational difficulties, it has not been applied to the F-Distribution. These problems have been overcome by making the standard transformation to the beta distribution.The procedure is explained in Sections 3 and 4. Empirical results of a comparison of CPU times are given in Section 5. The series expansion is compared to some of the standard root-finding methods. A table is given for p = .90.

Abernathy, Roger W.; Smith, Robert P.

doi: 10.1145/168173.168405pmid: N/A

Let 0 p 1 be given and let F be the cumulative distribution function of the F-Distribution with (M, N,) degrees of freedom. This FORTRAN 77 routine is a complement to [1] where a method was presented to find the inverse of the F-Distribution function, FINV(M, N, P), using a series expansion technique to find the inverse for the Beta Distribution function.

Abernathy, Roger W.; Smith, Robert P.

doi: 10.1145/168173.168405pmid: N/A

Let 0← p ←1 be given and let F be the cumulative distribution function of the F -Distribution with ( M, N, ) degrees of freedom. This FORTRAN 77 routine is a complement to 1 where a method was presented to find the inverse of the F -Distribution function, FINV( M, N, P ), using a series expansion technique to find the inverse for the Beta Distribution function.