ACM Transactions on Mathematical Software (TOMS)

Hall, George

doi: 10.1145/7921.7922pmid: N/A

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. This extends and generalizes the results of Part I of this paper, which deal with the real case. Familiarity with Part I is assumed, but not essential.

Enright, W. H.; Jackson, K. R.; Nørsett, S. P.; Thomsen, P. G.

doi: 10.1145/7921.7923pmid: N/A

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 subroutines RKF45 and DVERK. A typical result is that no extra function evaluations are required to obtain an interpolant with O ( h 5 ) local truncation error for the fifth-order RK formula used in RKF45; two extra function evaluations per step are required to obtain an interpolant with O ( h 6 ) local truncation error for this RK formula.

Kallay, Michael

doi: 10.1145/7921.7924pmid: N/A

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 length.

Skeel, Robert D.; Vu, Thu V.

doi: 10.1145/7921.7925pmid: N/A

Sagie, Ike

doi: 10.1145/7921.15667pmid: N/A

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 diversity and complexity of the available software inhibit the widespread use of computers for planning. The integrated Computer-Aided Modeling and Planning (CAMP) system offers a simple and coherent tool for the planner. A Data Definition Language provides the means for building data banks; a Model Definition Language provides the means for defining mathematical models featuring abstract linear programming, advanced array arithmetics, and assertions; a Picture Definition Language facilitates formation of tables and diagrams; a Text Definition Language combines word processing with illustrations of modeling results. The man-machine interface is based on interactive panels for controlling the planning process and on a command language for analyzing modeling results. A multilingual capability allows selection of the national language for interfacing with the system. The architecture of CAMP is presented, and its design, implementation, and use in regional planning are discussed.

Liu, Joseph W. H.

doi: 10.1145/7921.11325pmid: N/A

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 storage allows some large problems to be solved without having to use auxiliary storage for the working arrays. Even if the working arrays exceed the core size, it will reduce the amount of input-output traffic necessary to manipulate the working vectors. Experimental results are provided to demonstrate significant storage reduction on practical problems using the proposed techniques.

Amos, D. E.

doi: 10.1145/7921.214331pmid: N/A

This algorithm is a package of subroutines for Computing Bessel functions H v (1) ( z ), H v (2) ( z ), I v (z) , J v (z) , K v (z) , Y v (z) and Airy functions Ai( z ), Ai′( z ), Bi( z ), Bi′( z ) for orders v ≥0 and complex z in −ॠ<arg z ≤ॠ. Eight callable subroutines and their double-precision counterparts are provided. Exponential scaling and sequence generation are auxiliary options.

Nash, J. C.; Wang, R. L. C.

doi: 10.1145/7921.214334pmid: N/A

Crawford, Charles R.

doi: 10.1145/7921.214335pmid: N/A

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 structures used to store the matrices. The user must provide a subroutine, CHLSKY, which acts as an interface between PDFIND and the matrix data structures. CHLSKY also provides the user control over the number of iterations of the algorithm. Implementations of CHLSKY are included which call LINPAC routines for full matrices as well as symmetric banded matrices.

Hake, J.-Fr.

doi: 10.1145/7921.356181pmid: N/A