A TRIDIAGONALIZATION METHOD FOR SYMMETRIC SADDLE-POINT SYSTEMS

被引：3

作者：

Buttari, Alfredo ^{[1
]}

Orban, Dominique ^{[2
,3
]}

Ruiz, Daniel ^{[4
]}

Titley-Peloquin, David ^{[5
]}

机构：

[1] Univ Toulouse, CNRS, IRIT, F-31000 Toulouse, France

[2] Ecole Polytech, Gerad, Montreal, PQ H3C 3A7, Canada

[3] Ecole Polytech, Dept Math & Ind Engn, Montreal, PQ H3C 3A7, Canada

[4] Univ Toulouse, INPT, IRIT, F-31071 Toulouse, France

[5] McGill Univ, Dept Bioresource Engn, Ste Anne De Bellevue, PQ H9X 3V9, Canada

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2019年 / 41卷 / 05期

基金：

加拿大自然科学与工程研究理事会;

关键词：

symmetric saddle-point systems; iterative methods; orthogonal tridiagonalization; LINEAR-EQUATIONS; ALGORITHM; LSQR;

D O I：

10.1137/18M1194900

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose an iterative method for the solution of symmetric saddle-point systems that exploits the orthogonal tridiagonalization method of Saunders, Simon, and Yip (1988). By contrast with methods based on the Golub and Kahan (1965) bidiagonalization process, our method takes advantage of two initial vectors and splits the system into the sum of a least-squares and a least-norm problem. Our method typically requires fewer operator-vector products than MINRES, yet performs a comparable amount of work per iteration and has comparable storage requirements.

引用

页码：S409 / S432

页数：24

共 50 条

[31] Iterative Solution of Saddle-Point Systems of Linear Equations
Il’in V.P.
Kazantcev G.Y.
Journal of Mathematical Sciences, 2020, 249 (2) : 199 - 208
[32] Network Clustering: A Dynamical Systems and Saddle-Point Perspective
Buerger, Mathias
Zelazo, Daniel
Allgoewer, Frank
2011 50TH IEEE CONFERENCE ON DECISION AND CONTROL AND EUROPEAN CONTROL CONFERENCE (CDC-ECC), 2011, : 7825 - 7830
[33] GENERALIZED SADDLE-POINT METHOD FOR FESHBACH RESONANCES - COMMENT
CHUNG, KT
PHYSICAL REVIEW A, 1990, 41 (07): : 4090 - 4092
[34] GENERALIZED SADDLE-POINT METHOD FOR FESHBACH RESONANCES - REPLY
BYLICKI, M
PHYSICAL REVIEW A, 1990, 41 (07): : 4093 - 4094
[35] On preconditioner updates for sequences of saddle-point linear systems
De Simone, Valentian
di Serafino, Daniela
Morini, Benedetta
COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS, 2018, 9 (01): : 35 - 41
[36] OPTICAL-FIELD EFFECT ON THRESHOLDS SADDLE-POINT EDGES AND SADDLE-POINT EXCITIONS
PHILLIPS, JC
SERAPHIN, BO
PHYSICAL REVIEW LETTERS, 1965, 15 (03) : 107 - &
[37] SADDLE-POINT RESONANCES IN FEW-BODY SYSTEMS
ROST, JM
BRIGGS, JS
CHEMICAL PHYSICS LETTERS, 1991, 177 (03) : 321 - 325
[38] SADDLE-POINT COMPLEX-ROTATION METHOD FOR RESONANCES
CHUNG, KT
DAVIS, BF
PHYSICAL REVIEW A, 1982, 26 (06): : 3278 - 3282
[39] THE SADDLE-POINT METHOD IN CN AND THE GENERALIZED AIRY FUNCTIONS
Pinna, Francesco
Viola, Carlo
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 2019, 147 (02): : 221 - 257
[40] SADDLE-POINT VARIATIONAL METHOD FOR THE DIRAC-EQUATION
FRANKLIN, J
INTEMANN, RL
PHYSICAL REVIEW LETTERS, 1985, 54 (19) : 2068 - 2070

← 1 2 3 4 5 →