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Optimal preconditioners of a given sparsity pattern

https://doi.org/10.1007/bf01932737

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/978-3-642-05156-2openalex-snapshot

Matrix Iterative Analysis

inferredcites →https://doi.org/10.1007/bf01389752openalex-snapshot

Comparisons of regular splittings of matrices

inferredcites →https://doi.org/10.1007/bf01389760openalex-snapshot

A note on optimal block-scaling of matrices

inferredcites →https://doi.org/10.1007/bf01399553openalex-snapshot

Comparison of splittings used with the conjugate gradient algorithm

inferredcites →https://doi.org/10.1007/bf01931691openalex-snapshot

A class of first order factorization methods

inferredcites →https://doi.org/10.1007/bf02165096openalex-snapshot

Condition numbers and equilibration of matrices

inferredcites →https://doi.org/10.1007/bf02243566openalex-snapshot

Approximating the inverse of a matrix for use in iterative algorithms on vector processors

inferredcites →https://doi.org/10.1016/0024-3795(82)90014-3openalex-snapshot

Optimal block diagonal scaling of block 2-cyclic matrices

inferredcites →https://doi.org/10.1016/0024-3795(89)90285-1openalex-snapshot

Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences

inferredcites →https://doi.org/10.1016/0377-0427(84)90068-2openalex-snapshot

Fast approximate solution of large scale sparse linear systems

inferredcites →https://doi.org/10.1016/c2013-0-11733-3openalex-snapshot

Iterative Solution of Large Linear Systems

inferredcites →https://doi.org/10.1080/00207168408803441openalex-snapshot

Parallel algorithms for the solution of certain large sparse linear systems

inferredcites →https://doi.org/10.1080/00207169208804097openalex-snapshot

Approximate inverse preconditionings for sparse linear systems

inferredcites →https://doi.org/10.1090/s0002-9939-1955-0069585-4openalex-snapshot

On Best Conditioned Matrices

inferredcites →https://doi.org/10.1090/s0025-5718-1977-0431719-xopenalex-snapshot

Multi-Level Adaptive Solutions to Boundary-Value Problems

inferredcites →https://doi.org/10.1090/s0025-5718-1977-0438681-4openalex-snapshot

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

inferredcites →https://doi.org/10.1090/s0025-5718-1984-0758197-9openalex-snapshot

Decay Rates for Inverses of Band Matrices

inferredcites →https://doi.org/10.1137/0609021openalex-snapshot

On Minimizing the Maximum Eigenvalue of a Symmetric Matrix

inferredcites →https://doi.org/10.1137/0710092openalex-snapshot

Use of Fast Direct Methods for the Efficient Numerical Solution of Nonseparable Elliptic Equations

inferredcites →https://doi.org/10.1137/0720025openalex-snapshot

Polynomial Preconditioners for Conjugate Gradient Calculations

inferredcites →https://doi.org/10.1137/0720040openalex-snapshot

The Condition Number of Equivalence Transformations That Block Diagonalize Matrix Pencils

inferredcites →https://doi.org/10.1137/0721021openalex-snapshot

The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions

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

inferredcites →https://doi.org/10.1137/0724029openalex-snapshot

Analysis of Preconditioners for Domain Decomposition

inferredcites →https://doi.org/10.1515/rnam.1986.1.4.293openalex-snapshot

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

inferredcites →https://doi.org/10.2307/2003862openalex-snapshot

Matrix Iterative Analysis

inferredcites →https://doi.org/10.2307/2005542openalex-snapshot

Iterative Solution of Large Linear Systems

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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New convergence results and preconditioning strategies for the conjugate gradient method

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The convergence behaviour of iterative methods on severely stretched grids

inferred← citeshttps://doi.org/10.1007/978-1-4471-0807-8_6openalex-snapshot

Conditions for the existence and uniqueness of optimal matrix scalings

inferred← citeshttps://doi.org/10.1007/bf01582229openalex-snapshot

An interior-point method for fractional programs with convex constraints

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A numerical study of optimized sparse preconditioners

inferred← citeshttps://doi.org/10.1007/bf02074880openalex-snapshot

Towards a cost-effective ILU preconditioner with high level fill

inferred← citeshttps://doi.org/10.1007/s10589-026-00770-8openalex-snapshot

Scalable approximate optimal diagonal preconditioning

inferred← citeshttps://doi.org/10.1016/j.neucom.2014.05.015openalex-snapshot

Improvement of the convergence speed of a discrete-time recurrent neural network for quadratic optimization with general linear constraints

inferred← citeshttps://doi.org/10.1016/s0045-7949(98)00277-6openalex-snapshot

Problem-dependent preconditioners for iterative solvers in FE elastostatics

inferred← citeshttps://doi.org/10.1016/s0168-2024(99)80012-5openalex-snapshot

References

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Scalable preconditioned conjugate gradient inversion of vector finite element mass matrices

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Structured inverse eigenvalue problems

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Approximate inverse preconditionings for sparse linear systems

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Neural network for quadratic optimization with bound constraints

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Convergence analysis of a discrete-time recurrent neural network to perform quadratic real optimization with bound constraints

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A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints.

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Existence and uniqueness of optimal matrix scalings

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When Structure is Silent: Opportunities for Algorithmic Dispatch in Linear Algebra

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New Discrete-Time Recurrent Neural Network Proposal for Quadratic Optimization With General Linear Constraints

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An Algebraic Analysis of a Block Diagonal Preconditioner for Saddle Point Systems

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Minimizing the Condition Number for Small Rank Modifications

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The Interface Probing Technique in Domain Decomposition

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Diagonal Scalings of the Laplacian as Preconditioners for Other Elliptic Differential Operators

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Large-Scale Optimization of Eigenvalues

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Predict-and-Recompute Conjugate Gradient Variants

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On the Least Squares Solution of Inverse Eigenvalue Problems

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Inverse Eigenvalue Problems

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Existence and Uniqueness of Optimal Matrix Scalings

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On Optimal Banded Preconditioners for the Five-Point Laplacian

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Optimal Diagonal Preconditioning

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A Simple Proof of Gustafsson’s Conjecture in Case of Poisson Equation on Rectangular Domains

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Subspace-preserving sparsification of matrices with minimal perturbation to the near null-space. Part I: Basics

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Fast and Near-Optimal Diagonal Preconditioning

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