Results 1 
4 of
4
LARGESCALE LINEARLY CONSTRAINED OPTIMIZATION
, 1978
"... An algorithm for solving largescale nonlinear ' programs with linear constraints is presented. The method combines efficient sparsematrix techniques as in the revised simplex method with stable quasiNewton methods for handling the nonlinearities. A generalpurpose production code (MINOS) is descr ..."
Abstract

Cited by 75 (11 self)
 Add to MetaCart
An algorithm for solving largescale nonlinear ' programs with linear constraints is presented. The method combines efficient sparsematrix techniques as in the revised simplex method with stable quasiNewton methods for handling the nonlinearities. A generalpurpose production code (MINOS) is described, along with computational experience on a wide variety of problems.
Parallel algorithms for Toeplitz systems", Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms (edited by
 Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms
, 1991
"... We describe some parallel algorithms for the solution of Toeplitz linear systems and Toeplitz least squares problems. First we consider the parallel implementation of the Bareiss algorithm (which is based on the classical Schur algorithm). The alternative Levinson algorithm is less suited to paralle ..."
Abstract

Cited by 14 (7 self)
 Add to MetaCart
We describe some parallel algorithms for the solution of Toeplitz linear systems and Toeplitz least squares problems. First we consider the parallel implementation of the Bareiss algorithm (which is based on the classical Schur algorithm). The alternative Levinson algorithm is less suited to parallel implementation because it involves inner products. The Bareiss algorithm computes the LU factorization of the Toeplitz matrix T without pivoting, so can be unstable. For this reason, and also for the application to least squares problems, it is natural to consider algorithms for the QR factorization of T. The first O(n 2) serial algorithm for this problem was given by Sweet [5], but Sweet’s algorithm seems difficult to implement in parallel. Also, despite the fact that it computes an orthogonal factorization of T, Sweet’s algorithm can be numerically unstable. We describe an algorithm of Bojanczyk, Brent and de Hoog [1] for the QR factorization problem, and show that it is suitable for parallel implementation. This algorithm overcomes some (but not all) of the numerical difficulties of Sweet’s algorithm. We briefly compare some other algorithms, such as the “lattice ” algorithm of Cybenko and the “generalized Schur ” algorithm
Old and new algorithms for Toeplitz systems
 PROCEEDINGS SPIE, VOLUME 975, ADVANCED ALGORITHMS AND ARCHITECTURES FOR SIGNAL PROCESSING III (EDITED BY FRANKLIN T. LUK), SPIE
, 1989
"... Toeplitz linear systems and Toeplitz least squares problems commonly arise in digital signal processing. In this paper we survey some old, “well known” algorithms and some recent algorithms for solving these problems. We concentrate our attention on algorithms which can be implemented efficiently on ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
Toeplitz linear systems and Toeplitz least squares problems commonly arise in digital signal processing. In this paper we survey some old, “well known” algorithms and some recent algorithms for solving these problems. We concentrate our attention on algorithms which can be implemented efficiently on a variety of parallel machines (including pipelined vector processors and systolic arrays). We distinguish between algorithms which require inner products, and algorithms which avoid inner products, and thus are better suited to parallel implementation on some parallel architectures. Finally, we mention some “asymptotically fast” O(n(log n)²) algorithms and compare them with O(n²) algorithms.
NorthHolland Publishing Company MATRIX FACTOR1ZATIONS IN OPTIMIZATION OF NON LINEAR FUNCTIONS SUBJECT TO LINEAR CONSTRAINTS*
, 1974
"... Several ways of implementing methods for solving nonlinear optimization problems involving linear inequality and equality constraints using numerically stable matrix factorizations are described. The methods considered all follow an active constraint set approach and include quadratic programming, v ..."
Abstract
 Add to MetaCart
Several ways of implementing methods for solving nonlinear optimization problems involving linear inequality and equality constraints using numerically stable matrix factorizations are described. The methods considered all follow an active constraint set approach and include quadratic programming, variable metric, and modified Newton methods. 1.