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ACM Transactions on Mathematical Software (TOMS), Volume 12 Issue 3, Sept. 1986

Equilibrium states of Runge-Kutta schemes: part II
George Hall
Pages: 183-192
DOI: 10.1145/7921.7922
A theory is given that accounts for the observed behavior of Runge-Kutta codes when the stepsize is restricted by stability. The theory deals with the general case when the dominant eigenvalues of the Jacobian may be a complex conjugate pair....

Interpolants for Runge-Kutta formulas
W. H. Enright, K. R. Jackson, S. P. Nørsett, P. G. Thomsen
Pages: 193-218
DOI: 10.1145/7921.7923
A general procedure for the construction of interpolants for Runge-Kutta (RK) formulas is presented. As illustrations, this approach is used to develop interpolants for three explicit RK formulas, including those employed in the well-known...

Plane curves of minimal energy
Michael Kallay
Pages: 219-222
DOI: 10.1145/7921.7924
The problem of finding the plane curve of minimal elastic energy with prescribed endpoints and end-directions was solved in 1983 by B. K. P. Horn. Here the solution is discussed, given a very short proof, and extended to include a constant on...

Note on blended linear multistep formulas
Robert D. Skeel, Thu V. Vu
Pages: 223-224
DOI: 10.1145/7921.7925
The blended linear multistep methods of Skeel and Kong (1977) are fairly simply expressed in Nordsieck form, but the underlying multistep method turns out to be much more complicated. ...

Computer-aided modeling and planning (CAMP)
Ike Sagie
Pages: 225-248
DOI: 10.1145/7921.15667
Many planning methods are based on mathematical modeling. A multitude of computer aids covers different facets of the planning activity: data management, linear programming, statistical analysis, graphics, and word processing. However, the...

On the storage requirement in the out-of-core multifrontal method for sparse factorization
Joseph W. H. Liu
Pages: 249-264
DOI: 10.1145/7921.11325
Two techniques are introduced to reduce the working storage requirement for the recent multifrontal method of Duff and Reid used in the sparse out-of-core factorization of symmetric matrices. For a given core size, the reduction in working...

Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order
D. E. Amos
Pages: 265-273
DOI: 10.1145/7921.214331
This algorithm is a package of subroutines for Computing Bessel functions Hv(1)(z), Hv(2)(z),...

Algorithm 645: Subroutines for testing programs that compute the generalized inverse of a matrix
J. C. Nash, R. L. C. Wang
Pages: 274-277
DOI: 10.1145/7921.214334

Algorithm 646: PDFIND: a routine to find a positive definite linear combination of two real symmetric matrices
Charles R. Crawford
Pages: 278-282
DOI: 10.1145/7921.214335
PDFIND is a FORTRAN-77 implementation of an algorithm that finds a positive definite linear combination of two symmetric matrices, or determines that such a combination does not exist. The algorithm is designed to be independent of the data...

Remark on “Algorithm 569: COLSYS: Collocation Software for Boundary-Value ODEs [D2]”
J.-Fr. Hake
Pages: 283-284
DOI: 10.1145/7921.356181

Corrigendum: “A Note on Complex Division”
G. W. Stewart
Page: 285
DOI: 10.1145/7921.356182