Conjugate Gradient Algorithms in Nonconvex Optimization (Paperback, Softcover reprint of hardcover 1st ed. 2009)

Conjugate direction methods were proposed in the early 1950s. When high speed digital computing machines were developed, attempts were made to lay the fo- dations for the mathematical aspects of computations which could take advantage of the ef?ciency of digital computers. The National Bureau of Standards sponsored the Institute for Numerical Analysis, which was established at the University of California in Los Angeles. A seminar held there on numerical methods for linear equationswasattendedbyMagnusHestenes, EduardStiefel andCorneliusLanczos. This led to the ?rst communication between Lanczos and Hestenes (researchers of the NBS) and Stiefel (of the ETH in Zurich) on the conjugate direction algorithm. The method is attributed to Hestenes and Stiefel who published their joint paper in 1952 [101] in which they presented both the method of conjugate gradient and the conjugate direction methods including conjugate Gram-Schmidt processes. A closelyrelatedalgorithmwasproposedbyLanczos[114]whoworkedonalgorithms for determiningeigenvalues of a matrix. His iterative algorithm yields the similarity transformation of a matrix into the tridiagonal form from which eigenvalues can be well approximated.Thethree-termrecurrencerelationofthe Lanczosprocedurecan be obtained by eliminating a vector from the conjugate direction algorithm scheme. Initially the conjugate gradient algorithm was called the Hestenes-Stiefel-Lanczos method [86].

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Nonconvex Optimization and Its Applications, 89
Release date:	November 2010
First published:	2009
Authors:	Radoslaw Pytlak
Dimensions:	235 x 155 x 25mm (L x W x T)
Format:	Paperback
Pages:	478
Edition:	Softcover reprint of hardcover 1st ed. 2009
ISBN-13:	978-3-642-09925-0
Categories:	Books > Business & Economics > Business & management > Management & management techniques > Operational research Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Calculus of variations Books > Professional & Technical > Mechanical engineering & materials > Production engineering > Reliability engineering
LSN:	3-642-09925-4
Barcode:	9783642099250

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