Algorithm 809: PREQN: Fortran 77 subroutines for preconditioning the conjugate gradient method

José Luis Morales; Jorge Nocedal

doi:10.1145/382043.382343

Algorithm 809: PREQN: Fortran 77 subroutines for preconditioning the conjugate gradient method

José Luis Morales^*, Jorge Nocedal

^*Corresponding author for this work

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

PREQN is a package of Fortran 77 subroutines for automatically generating preconditioners for the conjugate gradient method. It is designed for solving a sequence of linear systems A_ix = b_i, i = 1, . . . , t, where the coefficient matrices A_i are symmetric and positive definite and vary slowly. Problems of this type arise, for example, in nonlinear optimization. The preconditioners are based on limited-memory quasi-Newton updating and are recommended for problems in which (i) the coefficient matrices are not explicitly known and only matrix-vector products of the form A_iv can be computed; or (ii) the coefficient matrices are not sparse. PREQN is written so that a single call from a conjugate gradient routine performs the preconditioning operation and stores information needed for the generation of a new preconditioner.

Original language	English (US)
Pages (from-to)	83-91
Number of pages	9
Journal	ACM Transactions on Mathematical Software
Volume	27
Issue number	1
DOIs	https://doi.org/10.1145/382043.382343
State	Published - Mar 2001

Keywords

G.1.3 [Numerical Analysis]: Numerical linear algebra - Linear systems (direct and iterative methods)
G.1.6 [Numerical Analysis]: Optimization - Gradient methods
Unconstrained optimization

ASJC Scopus subject areas

Software
Applied Mathematics

Access to Document

10.1145/382043.382343

Cite this

@article{b714e44813ab43c38759b80a3af9dc38,

title = "Algorithm 809: PREQN: Fortran 77 subroutines for preconditioning the conjugate gradient method",

abstract = "PREQN is a package of Fortran 77 subroutines for automatically generating preconditioners for the conjugate gradient method. It is designed for solving a sequence of linear systems Aix = bi, i = 1, . . . , t, where the coefficient matrices Ai are symmetric and positive definite and vary slowly. Problems of this type arise, for example, in nonlinear optimization. The preconditioners are based on limited-memory quasi-Newton updating and are recommended for problems in which (i) the coefficient matrices are not explicitly known and only matrix-vector products of the form Aiv can be computed; or (ii) the coefficient matrices are not sparse. PREQN is written so that a single call from a conjugate gradient routine performs the preconditioning operation and stores information needed for the generation of a new preconditioner.",

keywords = "G.1.3 [Numerical Analysis]: Numerical linear algebra - Linear systems (direct and iterative methods), G.1.6 [Numerical Analysis]: Optimization - Gradient methods, Unconstrained optimization",

author = "Morales, {Jos{\'e} Luis} and Jorge Nocedal",

year = "2001",

month = mar,

doi = "10.1145/382043.382343",

language = "English (US)",

volume = "27",

pages = "83--91",

journal = "ACM Transactions on Mathematical Software",

issn = "0098-3500",

publisher = "Association for Computing Machinery (ACM)",

number = "1",

}

TY - JOUR

T1 - Algorithm 809

T2 - PREQN: Fortran 77 subroutines for preconditioning the conjugate gradient method

AU - Morales, José Luis

AU - Nocedal, Jorge

PY - 2001/3

Y1 - 2001/3

N2 - PREQN is a package of Fortran 77 subroutines for automatically generating preconditioners for the conjugate gradient method. It is designed for solving a sequence of linear systems Aix = bi, i = 1, . . . , t, where the coefficient matrices Ai are symmetric and positive definite and vary slowly. Problems of this type arise, for example, in nonlinear optimization. The preconditioners are based on limited-memory quasi-Newton updating and are recommended for problems in which (i) the coefficient matrices are not explicitly known and only matrix-vector products of the form Aiv can be computed; or (ii) the coefficient matrices are not sparse. PREQN is written so that a single call from a conjugate gradient routine performs the preconditioning operation and stores information needed for the generation of a new preconditioner.

AB - PREQN is a package of Fortran 77 subroutines for automatically generating preconditioners for the conjugate gradient method. It is designed for solving a sequence of linear systems Aix = bi, i = 1, . . . , t, where the coefficient matrices Ai are symmetric and positive definite and vary slowly. Problems of this type arise, for example, in nonlinear optimization. The preconditioners are based on limited-memory quasi-Newton updating and are recommended for problems in which (i) the coefficient matrices are not explicitly known and only matrix-vector products of the form Aiv can be computed; or (ii) the coefficient matrices are not sparse. PREQN is written so that a single call from a conjugate gradient routine performs the preconditioning operation and stores information needed for the generation of a new preconditioner.

KW - G.1.3 [Numerical Analysis]: Numerical linear algebra - Linear systems (direct and iterative methods)

KW - G.1.6 [Numerical Analysis]: Optimization - Gradient methods

KW - Unconstrained optimization

UR - http://www.scopus.com/inward/record.url?scp=0011630080&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011630080&partnerID=8YFLogxK

U2 - 10.1145/382043.382343

DO - 10.1145/382043.382343

M3 - Article

AN - SCOPUS:0011630080

SN - 0098-3500

VL - 27

SP - 83

EP - 91

JO - ACM Transactions on Mathematical Software

JF - ACM Transactions on Mathematical Software

IS - 1

ER -

Algorithm 809: PREQN: Fortran 77 subroutines for preconditioning the conjugate gradient method

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this