Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems

H.A. van der Vorst

Type: Article

Publication Date: 1992-03-01

Citations: 5083

DOI: https://doi.org/10.1137/0913035

View Publication

Locations

SIAM Journal on Scientific and Statistical Computing - View

Similar Works

Action	Title	Year	Authors
+	Generalized conjugate gradient squared	1996	Diederik R. Fokkema Gérard L. G. Sleijpen H.A. van der Vorst
+	BiCR variants of the hybrid BiCG methods for solving linear systems with nonsymmetric matrices	2009	Kuniyoshi Abe Gérard L. G. Sleijpen
+	A composite step bi-conjugate gradient algorithm for nonsymmetric linear systems	1994	Randolph E. Bank Tony F. Chan
+	Conjugate gradient (CG)-type method for the solution of Newton's equation within optimization frameworks	2004	Giovanni Fasano
+	Variant Implementations of SCBiCG Method for Linear Equations with Complex Symmetric Matrices	2015	Kuniyoshi Abe Seiji Fujino
+ PDF Chat	An Augmented Conjugate Gradient Method for Solving Consecutive Symmetric Positive Definite Linear Systems	2000	Jocelyne Erhel Frédéric Guyomarc'h
+	A Smoothed Conjugate Residual Squared Algorithm for Solving Nonsymmetric Linear Systems	2009	Jing Zhao Jianhua Zhang
+	A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems	1994	Tony F. Chan Tedd Szeto
+	A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems	1994	Tony F. Chan Efstratios Gallopoulos Valeria Simoncini Tedd Szeto Christopher Tong
+	cPCG: Efficient and Customized Preconditioned Conjugate Gradient Method for Solving System of Linear Equations	2019
+	Conjugate gradient solution of linear equations	1998	Per Brinch Hansen
+ PDF Chat	A generalization of the method of conjugate gradients for solving systems of linear algebraic equations	1954	J. H. Curtiss
+	A Generalization of the Method of Conjugate Gradients for Solving Systems of Linear Algebraic Equations	1954	J. H. Curtiss
+	A generalized conjugate gradient method for non-symmetric systems of linear equations.	2007	Paul Concus Gene H. Golub
+	Generalized product-type methods based on bi-conjugate gradient (GPBiCG) for solving shifted linear systems	2016	Mehdi Dehghan Reza MohammadiArani
+	The matrix iterative methods for solving a class of generalized coupled Sylvester-conjugate linear matrix equations	2015	Yajun Xie Changfeng Ma
+ PDF Chat	A cooperative conjugate gradient method for linear systems permitting efficient multi-thread implementation	2017	Amit Bhaya Pierre‐Alexandre Bliman Guilherme Niedu Fernando Pazos
+	GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems	1997	Shao‐Liang Zhang
+	The conjugate-gradient method for solving linear systems	1956	Magnus R. Hestenes
+ PDF Chat	A cooperative conjugate gradient method for linear systems permitting multithread implementation of low complexity	2012	Amit Bhaya Pierre‐Alexandre Bliman Guilherme Niedu Fernando Pazos

Works That Cite This (1540)

Action	Title	Year	Authors
+	Parallelism and Iterative bi-Lanczos Solvers	2021	Josip Bašić Branko Blagojević Martina Bašić Marjan Sikora
+	Bi-CGSTAB(L)法におけるLの動的選択について	2001	努宮内祥司伊藤紹良張亮名取
+	Computations on preconditioning cubic spline collocation method of elliptic equations	2001	Yong‐Hun Lee
+	Serial and Parallel Krylov Methods for Implicit Finite Difference Schemes Arising in Multivariate Option Pricing	2001	Manfred Gilli Evis Këllezi Giorgio Pauletto
+	Lanczos methods in economic Models: visual representation and computing	2004	Concepción González‐Concepción P. R. Graves-Morris
+	IDR(s)-SOR法の提案	2010	藤野清次 P. Sonneveld 尾上勇介 Martin B. van Gijzen
+ PDF Chat	A Genuinely Hybrid, Multiscale 3D Cancer Invasion and Metastasis Modelling Framework	2024	Dimitrios Katsaounis Nicholas Harbour Thomas Williams Mark A. J. Chaplain Nikolaos Sfakianakis
+	A partial proximal point algorithm for nuclear norm regularized matrix least squares problems	2014	Kaifeng Jiang Defeng Sun Kim-Chuan Toh
+	An element-by-element BICGSTAB iterative method for three-dimensional steady Navier-Stokes equations	1997	Morten M. T. Wang Tony W. H. Sheu
+ PDF Chat	Iterative solution of linear systems in the 20th century	2001	Yousef Saad H.A. van der Vorst

Works Cited by This (5)

Action	Title	Year	Authors
+	Conjugate gradient methods for indefinite systems	1976	R. Fletcher
+	A class of first order factorization methods	1978	Ivar Gustafsson
+	A comparison of direct and preconditioned iterative techniques for sparse, unsymmetric systems of linear equations	1989	G. Brussino V. Sonnad
+ PDF Chat	GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems	1986	Yousef Saad Martin H. Schultz
+	A Lanczos Method for a Class of Nonsymmetric Systems of Linear Equations	1978	Olof B. Widlund