Iterative Methods for Sparse Linear Systems

Matrix computations

1983 • 31,414 citations

Reducibility among Combinatorial Problems

1972 • 10,743 citations

GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems

1986 • 10,699 citations

The Theory of Matrices

1984 • 8,921 citations

Methods of conjugate gradients for solving linear systems

1952 • 7,639 citations

The algebraic eigenvalue problem

1965 • 5,953 citations

Matrix Iterative Analysis

2000 • 5,826 citations

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

1992 • 5,070 citations

An iteration method for the solution of the eigenvalue problem of linear differential and integral operators

1950 • 4,159 citations

Numerical Computation of Internal and External Flows

2007 • 3,528 citations

The Symmetric Eigenvalue Problem

1998 • 3,238 citations

Introduction to matrix computations

1973 • 2,448 citations

An Introduction to the Conjugate Gradient Method Without the Agonizing Pain

1994 • 2,220 citations

Introduction to Approximation Theory

1969 • 2,111 citations

Iterative Solution Methods

1994 • 2,108 citations

Iterative Solution of Large Linear Systems

1973 • 2,037 citations

Multi-grid methods and applications.

1986 • 1,958 citations

Introduction to the Numerical Solution of Markov Chains

1995 • 1,763 citations

The principle of minimized iterations in the solution of the matrix eigenvalue problem

1951 • 1,725 citations

Numerical Methods for Large Eigenvalue Problems

1992 • 1,719 citations

Partitioning Sparse Matrices with Eigenvectors of Graphs

1990 • 1,679 citations

Direct Methods for Sparse Matrices

2017 • 1,634 citations

An iterative solution method for linear systems of which the coefficient matrix is a symmetric 𝑀-matrix

1977 • 1,435 citations

A Flexible Inner-Outer Preconditioned GMRES Algorithm

1993 • 1,383 citations

Parallel and distributed computation

1989 • 1,225 citations

CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems

1989 • 1,142 citations

Finite Dimensional Vector Spaces

2018 • 1,139 citations

Iterative Methods by Space Decomposition and Subspace Correction

1992 • 1,135 citations

QMR: a quasi-minimal residual method for non-Hermitian linear systems

1991 • 952 citations

The incomplete Cholesky—conjugate gradient method for the iterative solution of systems of linear equations

1978 • 936 citations

Solution of systems of linear equations by minimized iterations

1952 • 896 citations

Interpolation and Approximation.

1965 • 834 citations

SPARSKIT: A basic tool kit for sparse matrix computations

1990 • 650 citations

Sparse matrix test problems

1989 • 649 citations

A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems

1993 • 621 citations

Introduction to Parallel and Vector Solution of Linear Systems

1988 • 585 citations

Domain decomposition algorithms

1994 • 575 citations

Sparse Matrix Technology

1984 • 556 citations

Padé-Type Approximation and General Orthogonal Polynomials

1980 • 547 citations

The Construction of Preconditioners for Elliptic Problems by Substructuring. I

1986 • 545 citations

An Improved Spectral Graph Partitioning Algorithm for Mapping Parallel Computations

1995 • 486 citations

Extrapolation Methods: Theory and Practice.

1993 • 486 citations

Krylov subspace methods for solving large unsymmetric linear systems

1981 • 448 citations

Solving Linear Systems on Vector and Shared Memory Computers.

1992 • 442 citations

Computational Variants of the Lanczos Method for the Eigenproblem

1972 • 403 citations

Iterative Methods for the Solution of Elliptic Problems on Regions Partitioned into Substructures

1986 • 399 citations

Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory.

1992 • 389 citations

On Generating Orthogonal Polynomials

1982 • 385 citations

Block Preconditioning for the Conjugate Gradient Method

1985 • 362 citations

Conjugate Gradient-Type Methods for Linear Systems with Complex Symmetric Coefficient Matrices

1992 • 362 citations

Implicit parallel processing in structural mechanics

1994 • 356 citations

Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods

1980 • 319 citations

Orthomin, an Iterative Method for Solving Sparse Sets of Simultaneous Linear Equations

1976 • 310 citations

Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods

1961 • 299 citations

Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method

1984 • 294 citations

Solution of Partial Differential Equations on Vector and Parallel Computers

1985 • 286 citations

GMRESR: a family of nested GMRES methods

1994 • 285 citations

Approximate Inverse Preconditioners via Sparse-Sparse Iterations

1998 • 263 citations

Implementation of the GMRES Method Using Householder Transformations

1988 • 261 citations

Krylov Subspace Methods on Supercomputers

1989 • 249 citations

Accelerated projection methods for computing pseudoinverse solutions of systems of linear equations

1979 • 230 citations

Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics

1967 • 229 citations

Finite element analysis of the compressible Euler and Navier-Stokes equations

1989 • 222 citations

Extrapolation Methods for Vector Sequences

1987 • 214 citations

Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations

1980 • 209 citations

Polynomial Preconditioners for Conjugate Gradient Calculations

1983 • 202 citations

Practical Use of Polynomial Preconditionings for the Conjugate Gradient Method

1985 • 189 citations

A Generalized Conjugate Gradient Method for Nonsymmetric Systems of Linear Equations

1976 • 187 citations

A Comparison of Domain Decomposition Techniques for Elliptic Partial Differential Equations and their Parallel Implementation

1987 • 185 citations

Large-scale vectorized implicit calculations in solid mechanics on a Cray X-MP/48 utilizing EBE preconditioned conjugate gradients

1987 • 182 citations

The Lanczos Biorthogonalization Algorithm and Other Oblique Projection Methods for Solving Large Unsymmetric Systems

1982 • 177 citations

A Lanczos Method for a Class of Nonsymmetric Systems of Linear Equations

1978 • 177 citations

Some Domain Decomposition Algorithms for Elliptic Problems

1990 • 174 citations

Direct Methods for Sparse Matrices

1980 • 152 citations

An Iterative Method for Elliptic Problems on Regions Partitioned into Substructures

1986 • 150 citations

A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms. Part II

1994 • 148 citations

An Iterative Method for Nonsymmetric Systems with Multiple Right-Hand Sides

1995 • 145 citations

A generalized SSOR method

1972 • 141 citations

Solving Sparse Symmetric Sets of Linear Equations by Preconditioned Conjugate Gradients

1980 • 140 citations

Implicit Solvers for Unstructured Meshes

1993 • 140 citations

A Theoretical Comparison of the Arnoldi and GMRES Algorithms

1991 • 140 citations

Implementation aspects of band Lanczos algorithms for computation of eigenvalues of large sparse symmetric matrices

1979 • 132 citations

On the Lánczos method for solving symmetric linear systems with several right-hand sides

1987 • 124 citations

Domain decomposition methods for large linearly elliptic three-dimensional problems

1991 • 120 citations

A Conjugate Gradient-Truncated Direct Method for the Iterative Solution of the Reservoir Simulation Pressure Equation

1981 • 119 citations

A Black Box Generalized Conjugate Gradient Solver with Inner Iterations and Variable-Step Preconditioning

1991 • 114 citations

Approximate inverse preconditionings for sparse linear systems

1992 • 113 citations

A Stability Analysis of Incomplete LU Factorizations

1986 • 112 citations

Automatic Mesh Partitioning

1993 • 110 citations

A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems

1994 • 110 citations

Approximation theory and numerical linear algebra

1990 • 107 citations

Large tridiagonal and block tridiagonal linear systems on vector and parallel computers

1987 • 104 citations

Row Projection Methods for Large Nonsymmetric Linear Systems

1992 • 102 citations

The convergence of inexact Chebyshev and Richardson iterative methods for solving linear systems

1988 • 98 citations

A breakdown-free Lanczos type algorithm for solving linear systems

1992 • 97 citations

Ordering Methods for Preconditioned Conjugate Gradient Methods Applied to Unstructured Grid Problems

1992 • 97 citations

Breadth-First Search

1984 • 95 citations

Is SOR Color-Blind?

1986 • 92 citations

Matrix multiplication by diagonals on a vector/parallel processor

1976 • 90 citations

A Fast Algorithm for Reordering Sparse Matrices for Parallel Factorization

1989 • 90 citations

A MIMD implementation of a parallel Euler solver for unstructured grids

1992 • 90 citations

Avoiding breakdown and near-breakdown in Lanczos type algorithms

1991 • 89 citations

Multicolor ICCG Methods for Vector Computers

1987 • 88 citations

Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering

1995 • 87 citations

Residual Smoothing Techniques for Iterative Methods

1994 • 86 citations

Parallel Algorithms for Matrix Computations

1990 • 81 citations

The Interface Probing Technique in Domain Decomposition

1992 • 81 citations

On Vectorizing Incomplete Factorization and SSOR Preconditioners

1988 • 81 citations

A Computation Model of Parallel Solution of Linear Equations

1980 • 79 citations

Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations

1991 • 72 citations

On some versions of incomplete block-matrix factorization iterative methods

1984 • 71 citations

Geometric mesh partitioning: implementation and experiments

2002 • 71 citations

Iterative methods for cyclically reduced nonselfadjoint linear systems

1990 • 71 citations

Theory of Gradient Methods

1959 • 67 citations

An Optimal Domain Decomposition Preconditioner for the Finite Element Solution of Linear Elasticity Problems

1992 • 67 citations

Accelerating with rank-one updates

1989 • 64 citations

Extrapolation vs. projection methods for linear systems of equations

1988 • 63 citations

SOLVING ELLIPTIC PROBLEMS ON REGIONS PARTITIONED INTO SUBSTRUCTURES

1984 • 63 citations

An analysis of the composite step biconjugate gradient method

1993 • 57 citations

A projection method for solving nonsymmetric linear systems on multiprocessors

1989 • 52 citations

CIMGS: An Incomplete Orthogonal FactorizationPreconditioner

1997 • 50 citations

Iterative algorithms for large sparse linear systems on parallel computers

1983 • 47 citations

Iterative Solution of Indefinite Symmetric Linear Systems by Methods Using Orthogonal Polynomials over Two Disjoint Intervals

1983 • 47 citations

Ordering techniques for the preconditioned conjugate gradient method on parallel computers

1989 • 45 citations

A stable Richardson iteration method for complex linear systems

1989 • 42 citations

Fast secant methods for the iterative solution of large nonsymmetric linear systems

1990 • 41 citations

Chebyshev polynomials are not always optimal

1991 • 41 citations

On a family of two-level preconditionings of the incomplete block factorization type

1986 • 40 citations

A Matrix Decomposition Method for Orthotropic Elasticity Problems

1989 • 39 citations

Parallel Preconditioning and Approximate Inverses on the Connection Machine.

1993 • 38 citations

On the Relationship between Overlapping and Nonoverlapping Domain Decomposition Methods

1992 • 34 citations

Highly Parallel Preconditioners for General Sparse Matrices

1994 • 34 citations

An optimum iterative method for solving any linear system with a square matrix

1988 • 34 citations

EFFICIENT ICCG ON A SHARED MEMORY MULTIPROCESSOR

1992 • 33 citations

DQGMRES: a Direct Quasi-minimal Residual Algorithm Based on Incomplete Orthogonalization

1996 • 33 citations

Analysis of some vector extrapolation methods for solving systems of linear equations

1995 • 32 citations

A parallel hybrid sparse linear system solver

1990 • 31 citations

Mapping Algorithms and Software Environment for Data Parallel PDE Iterative Solvers

1994 • 30 citations

Parallelizing preconditioned conjugate gradient algorithms

1989 • 30 citations

SOR as a preconditioner

1995 • 29 citations

Application of MACSYMA and sparse matrix technology to multielement airfoil calculations

1987 • 28 citations

An experimental study of methods for parallel preconditioned Krylov methods

1988 • 27 citations

Quasi-Kernel Polynomials and Convergence Results for Quasi-Minimal Residual Iterations

1992 • 25 citations

Chebyshev polynomials in the solution of large-scale linear systems

1952 • 25 citations

Manipulation and Visualization of Sparse Matrices

1990 • 25 citations

Orderings for Conjugate Gradient Preconditionings

1991 • 23 citations

Advanced Computer Architecture with Parallel Programming

1993 • 23 citations

On the constrained Chebyshev approximation problem on ellipses

1990 • 22 citations

A look-ahead variant of the lanczos algorithm and its application to the quasi-minimal residual method for non-hermitian linear systems

1991 • 20 citations

Krylov methods preconditioned with incompletely factored matrices on the CM-2

1990 • 19 citations

Efficient Implementations of Certain Iterative Methods

1988 • 17 citations

A theoretical overview of Krylov subspace methods

1995 • 16 citations

DOMAIN DECOMPOSER: A Software Tool for Mapping PDE Computations to Parallel Architectures

1990 • 15 citations

Acceleration of the outer conjugate gradient by reorthogonalization for a domain decomposition method for structural analysis problems

1989 • 15 citations

A robust parallel solver for block tridiagonal systems

1988 • 8 citations

A parallel algorithm for sparse unsymmetric lu factorization

1989 • 7 citations

4. Parallel Implicit Methods for Aerodynamic Applications on Unstructured Grids

1995 • 5 citations

Deleted Work

1955 • 0 citations