scholarly journals A Power Schur Complement Low-Rank Correction Preconditioner for General Sparse Linear Systems

2021 ◽  
Vol 42 (2) ◽  
pp. 659-682
Author(s):  
Qingqing Zheng ◽  
Yuanzhe Xi ◽  
Yousef Saad
Keyword(s):  
Linear Systems ◽  
Schur Complement ◽  
Low Rank ◽  
Sparse Linear Systems

Multicolor low‐rank preconditioner for general sparse linear systems

2020 ◽  
Vol 27 (4) ◽  
Author(s):  
Qingqing Zheng ◽  
Yuanzhe Xi ◽  
Yousef Saad
Keyword(s):  
Linear Systems ◽  
Low Rank ◽  
Sparse Linear Systems

A Hierarchical Low Rank Schur Complement Preconditioner for Indefinite Linear Systems

2018 ◽  
Vol 40 (4) ◽  
pp. A2234-A2252 ◽  
Author(s):  
Geoffrey Dillon ◽  
Vassilis Kalantzis ◽  
Yuanzhe Xi ◽  
Yousef Saad
Keyword(s):  
Linear Systems ◽  
Schur Complement ◽  
Low Rank ◽  
Indefinite Linear Systems

Parallel algorithm for solving sparse linear systems

1996 ◽  
Vol 32 (19) ◽  
pp. 1766
Author(s):  
K.N. Balasubramanya Murthy ◽  
C. Siva Ram Murthy
Keyword(s):  
Parallel Algorithm ◽  
Linear Systems ◽  
Sparse Linear Systems

Discretisation of sparse linear systems: An optimisation approach

2015 ◽  
Vol 80 ◽  
pp. 42-49 ◽  
Author(s):  
M. Souza ◽  
J.C. Geromel ◽  
P. Colaneri ◽  
R.N. Shorten
Keyword(s):  
Linear Systems ◽  
Sparse Linear Systems

scholarly journals Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

2012 ◽  
Vol 20 (3) ◽  
pp. 241-255 ◽  
Author(s):  
Eric Bavier ◽  
Mark Hoemmen ◽  
Sivasankaran Rajamanickam ◽  
Heidi Thornquist
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Sparse Matrix ◽  
Sparse Matrices ◽  
Direct Methods ◽  
Iterative Solvers ◽  
Software Project ◽  
Sparse Linear Systems ◽  
Scalar Type ◽  
Mixed Precision

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples the algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.

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