#### ACM Transactions on Mathematical Software (TOMS), Volume 23 Issue 4, Dec. 1997

**Algorithm 775**: the code SLEUTH for solving fourth-order Sturm-Liouville problems

Leon Greenberg, Marco Marletta

Pages: 453-493

DOI: 10.1145/279232.279231

We describe a new code (SLEUTH) for numerical solution of regular two-point fourth-order Sturm-Liouvlle eigenvalue problems. Eigenvalues are computed according to index: the user specifies an integer k***0, and the code computes...

**Algorithm 776: SRRIT**: a Fortran subroutine to calculate the dominant invariant subspace of a nonsymmetric matrix

Z. Bai, G. W. Stewart

Pages: 494-513

DOI: 10.1145/279232.279234

SRRT is a Fortran program to calculate an approximate orthonomral basis fr a dominant invariant subspace of a real matrix A by the method of simultaneous iteration. Specifically, given an integer m, SRRIT...

**Algorithm 777: HOMPACK90**: a suite of Fortran 90 codes for globally convergent homotopy algorithms

Layne T. Watson, Maria Sosonkina, Robert C. Melville, Alexander P. Morgan, Homer F. Walker

Pages: 514-549

DOI: 10.1145/279232.279235

**Algorithm 778: L-BFGS-B**: Fortran subroutines for large-scale bound-constrained optimization

Ciyou Zhu, Richard H. Byrd, Peihuang Lu, Jorge Nocedal

Pages: 550-560

DOI: 10.1145/279232.279236

L-BFGS-B is a limited-memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables. It is intended for problems in which information on the Hessian matrix is difficult to obtain, or for large dense...

**High-precision division and square root**

Alan H. Karp, Peter Markstein

Pages: 561-589

DOI: 10.1145/279232.279237

We present division and square root algorithm for calculations with more bits than are handled by the floating-point hardware. These algorithms avoid the need to multiply two high-precision numbers, speeding up the last iteration by as much as a...