GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
SIAM Journal on Scientific Computing
Hitting the memory wall: implications of the obvious
ACM SIGARCH Computer Architecture News
Block algorithms for sparse matrix computations on high performance workstations
ICS '96 Proceedings of the 10th international conference on Supercomputing
An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization
SIAM Journal on Matrix Analysis and Applications
A combined unifrontal/multifrontal method for unsymmetric sparse matrices
ACM Transactions on Mathematical Software (TOMS)
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination
SIAM Journal on Matrix Analysis and Applications
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
A Block Orthogonalization Procedure with Constant Synchronization Requirements
SIAM Journal on Scientific Computing
GMRES with Deflated Restarting
SIAM Journal on Scientific Computing
Truncation Strategies for Optimal Krylov Subspace Methods
SIAM Journal on Numerical Analysis
PASTIX: a high-performance parallel direct solver for sparse symmetric positive definite systems
Parallel Computing - Parallel matrix algorithms and applications
A Block Algorithm for Orthogonalization in Elliptic Norms
CONPAR '92/ VAPP V Proceedings of the Second Joint International Conference on Vector and Parallel Processing: Parallel Processing
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
Algorithms for Quad-Double Precision Floating Point Arithmetic
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
Reverse Communication Interface for Linear Algebra Templates for Iterative Methods
Reverse Communication Interface for Linear Algebra Templates for Iterative Methods
LAPACK Working Note 112: Practical Experience in the Dangers ofHeterogeneous Computing
LAPACK Working Note 112: Practical Experience in the Dangers ofHeterogeneous Computing
Optimizing the performance of sparse matrix-vector multiplication
Optimizing the performance of sparse matrix-vector multiplication
A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Sparsity: Optimization Framework for Sparse Matrix Kernels
International Journal of High Performance Computing Applications
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Recycling Krylov Subspaces for Sequences of Linear Systems
SIAM Journal on Scientific Computing
On the design of interfaces to sparse direct solvers
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
Block Gram-Schmidt Orthogonalization
SIAM Journal on Scientific Computing
A view of the parallel computing landscape
Communications of the ACM - A View of Parallel Computing
SIAM Journal on Scientific Computing
AMESOS: a set of general interfaces to sparse direct solver libraries
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Algorithm 907: KLU, A Direct Sparse Solver for Circuit Simulation Problems
ACM Transactions on Mathematical Software (TOMS)
Communication-avoiding krylov subspace methods
Communication-avoiding krylov subspace methods
A Communication-Avoiding, Hybrid-Parallel, Rank-Revealing Orthogonalization Method
IPDPS '11 Proceedings of the 2011 IEEE International Parallel & Distributed Processing Symposium
ShyLU: A Hybrid-Hybrid Solver for Multicore Platforms
IPDPS '12 Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium
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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.