#### ACM Transactions on Mathematical Software (TOMS), Volume 15 Issue 4, Dec. 1989

**The influence of relaxed supernode partitions on the multifrontal method**

Cleve Ashcraft, Roger Grimes

Pages: 291-309

DOI: 10.1145/76909.76910

In this paper we present an algorithm for partitioning the nodes of a graph into supernodes, which improves the performance of the multifrontal method for the factorization of large, sparse matrices on vector computers. This new algorithm first...

**The multifrontal method and paging in sparse Cholesky factorization**

Joseph W. H. Liu

Pages: 310-325

DOI: 10.1145/76909.76911

In this paper, we show that the multifrontal method can have significant advantage over the conventional sparse column-Cholesky scheme on a paged virtual memory system. A more than tenfold reduction in paging activities can be achieved, which...

**A comparison of adaptive refinement techniques for elliptic problems**

William F. Mitchell

Pages: 326-347

DOI: 10.1145/76909.76912

Adaptive refinement has proved to be a useful tool for reducing the size of the linear system of equations obtained by discretizing partial differential equations. We consider techniques for the adaptive refinement of triangulations used with...

**Algorithm 676: ODRPACK: software for weighted orthogonal distance regression**

Paul T. Boggs, Janet R. Donaldson, Richaard h. Byrd, Robert B. Schnabel

Pages: 348-364

DOI: 10.1145/76909.76913

In this paper, we describe ODRPACK, a software package for the weighted orthogonal distance regression problem. This software is an implementation of the algorithm described in [2] for finding the parameters that minimize the sum of the squared...

**Algorithm 677 ***C*^{1} surface interpolation

Laura Bacchelli Montefusco, Giulio Casciola

Pages: 365-374

DOI: 10.1145/76909.76914

**Indefinite integration with validation**

George Corliss, Gary Krenz

Pages: 375-393

DOI: 10.1145/76909.76915

We present an overview of two approaches to validated one-dimensional indefinite integration. The first approach is to find an inclusion of the integrand, then integrate this inclusion to obtain an inclusion of the indefinite integral....

**Algorithm 678: BTPEC: sampling from the binomial distribution**

Voratas Kachitvichyanukul, Bruce W. Schmeiser

Pages: 394-397

DOI: 10.1145/76909.76916

The FORTRAN implementation of an exact, uniformly fast algorithm for generating the binomial, random variables is presented. The algorithm is numerically stable and is faster than other published algorithms. The code uses only standard FORTRAN...