On the rate of convergence of the preconditioned conjugate gradient method
Numerische Mathematik
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A generalized conjugate gradient, least square method
Numerische Mathematik
Deflation of conjugate gradients with applications to boundary value problems
SIAM Journal on Numerical Analysis
An algebraic theory for multigrid methods for variational problems
SIAM Journal on Numerical Analysis
Algebraic multilevel preconditioning methods, II
SIAM Journal on Numerical Analysis
The convergence behaviour of preconditioned CG and CG-S in the presence of rounding errors
Proceedings of a conference on Preconditioned conjugate gradient methods
Chebyshev polynomials are not always optimal
Journal of Approximation Theory
SIAM Journal on Scientific and Statistical Computing
Predicting the behavior of finite precision Lanczos and conjugate gradient computations
SIAM Journal on Matrix Analysis and Applications
Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Convergence of iterations for linear equations
Convergence of iterations for linear equations
Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Iterative solution methods
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
SIAM Journal on Scientific Computing
On computing certain elements of the inverse of a sparse matrix
Communications of the ACM
Finite element solution of boundary value problems: theory and computation
Finite element solution of boundary value problems: theory and computation
SIAM Journal on Matrix Analysis and Applications
Flexible Inner-Outer Krylov Subspace Methods
SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Preconditioning of Boundary Value Problems Using Elementwise Schur Complements
SIAM Journal on Matrix Analysis and Applications
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Iterative solution methods to solve linear systems of equations were originally formulated as basic iteration methods of defectcorrection type, commonly referred to as Richardson's iteration method. These methods developed further into various versions of splitting methods, including the successive overrelaxation (SOR) method. Later, immensely important developments included convergence acceleration methods, such as the Chebyshev and conjugate gradient iterationmethods and preconditioning methods of various forms. A major strive has been to find methods with a total computational complexity of optimal order, that is, proportional to the degrees of freedom involved in the equation. Methods that have turned out to have been particularly important for the further developments of linear equation solvers are surveyed. Some of them are presented in greater detail.