On the public citation graph

Iterative refinement implies numerical stability

https://doi.org/10.1007/bf01932150

0 signed · 71 inferred · view as graph

Inferred edges come from two machine sources: sweeps of open repository metadata (mostly SSRN and Zenodo), and a bulk OpenAlex citation snapshot. Every row below is labelled with the one it came from. Neither is a complete citation index — absence here is not evidence of absence.

Is this your work? Sign in with ORCID and put your name on the claims that are yours.

Claim with ORCID

Reference health. See whether every reference in this work resolves to a known work and none has been retracted — and get a dated CiteStamped badge you can embed.

See reference health

What this work says

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

inferredcites →https://doi.org/10.1007/bf01933236openalex-snapshot

Iterative improvement without double precision in a boundary value problem

inferredcites →https://doi.org/10.1007/bf01934122openalex-snapshot

Solving linear least squares problems by Gram-Schmidt orthogonalization

inferredcites →https://doi.org/10.1016/0016-0032(64)90390-4openalex-snapshot

Rounding errors in algebraic processes

inferredcites →https://doi.org/10.1038/202016a0openalex-snapshot

Rounding Errors in Algebraic Processes

inferredcites →https://doi.org/10.1145/321386.321394openalex-snapshot

Iterative Refinement in Floating Point

inferredcites →https://doi.org/10.2307/2003558openalex-snapshot

The Algebraic Eigenvalue Problem

What points at this work

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

inferred← citeshttps://doi.org/10.1002/nla.2434openalex-snapshot

Multistage mixed precision iterative refinement

inferred← citeshttps://doi.org/10.1007/978-1-4613-8351-2_3openalex-snapshot

Componentwise Error Analysis for Stationary Iterative Methods

inferred← citeshttps://doi.org/10.1007/978-1-4684-7324-7_6openalex-snapshot

Multiple Shooting Techniques Revisited

inferred← citeshttps://doi.org/10.1007/978-3-642-41591-3_14openalex-snapshot

Scalability Tests of a Finite Element Code on Hundreds of Thousands Cores and Heterogeneous Architecture

inferred← citeshttps://doi.org/10.1007/978-981-95-7093-5_10openalex-snapshot

Iterative Coordinate Partitioning Method for Enhanced Multibody Dynamics Simulation

inferred← citeshttps://doi.org/10.1007/bf00944965openalex-snapshot

A recursive algorithm for the incomplete partial fraction decomposition

inferred← citeshttps://doi.org/10.1007/bf01385630openalex-snapshot

Bordered augmented linear systems in numerical continuation and bifurcation

inferred← citeshttps://doi.org/10.1007/bf01411845openalex-snapshot

Round-off error analysis of iterations for large linear systems

inferred← citeshttps://doi.org/10.1007/bf01931663openalex-snapshot

Block elimination with one refinement solves bordered linear systems accurately

inferred← citeshttps://doi.org/10.1007/bf01933262openalex-snapshot

Iterative refinement enhances the stability ofQR factorization methods for solving linear equations

inferred← citeshttps://doi.org/10.1007/bf01936142openalex-snapshot

The accurate solution of certain continuous problems using only single precision arithmetic

inferred← citeshttps://doi.org/10.1007/bf02140689openalex-snapshot

Rank-k modification methods for recursive least squares problems

inferred← citeshttps://doi.org/10.1007/bf02140770openalex-snapshot

Stability analysis of a general toeplitz systems solver

inferred← citeshttps://doi.org/10.1007/bf03186544openalex-snapshot

Iterative refinement for ill-conditioned linear systems

inferred← citeshttps://doi.org/10.1007/s00366-025-02187-zopenalex-snapshot

Mixed precision iterative refinement with adaptive precision sparse approximate inverse preconditioning

inferred← citeshttps://doi.org/10.1007/s11075-023-01596-9openalex-snapshot

Acceleration of iterative refinement for singular value decomposition

inferred← citeshttps://doi.org/10.1007/s11831-014-9095-yopenalex-snapshot

Simulation at Extreme-Scale: Co-Design Thinking and Practices

inferred← citeshttps://doi.org/10.1016/0024-3795(80)90259-1openalex-snapshot

Roundoff-error analysis of a new class of conjugate-gradient algorithms

inferred← citeshttps://doi.org/10.1016/0024-3795(87)90101-7openalex-snapshot

Stability analysis of the method of seminormal equations for linear least squares problems

inferred← citeshttps://doi.org/10.1016/0024-3795(88)90197-8openalex-snapshot

The simplex method is not always well behaved

inferred← citeshttps://doi.org/10.1016/0045-7825(93)90079-dopenalex-snapshot

Accuracy and effectiveness of preconditioned conjugate gradient algorithms for large and ill-conditioned problems

inferred← citeshttps://doi.org/10.1016/b978-0-12-068780-0.50012-1openalex-snapshot

Direct Methods for Solving Finite Element Equations

inferred← citeshttps://doi.org/10.1016/b978-0-12-497250-6.50010-8openalex-snapshot

BIBLIOGRAPHY

inferred← citeshttps://doi.org/10.1016/j.amc.2005.11.131openalex-snapshot

An effective predictor–corrector process for large scale linear system of equations

inferred← citeshttps://doi.org/10.1016/j.amc.2006.05.075openalex-snapshot

Note on predictor–corrector process for ill-conditioned linear system of equations

inferred← citeshttps://doi.org/10.1016/j.amc.2007.04.007openalex-snapshot

Wilkinson’s iterative refinement of solution with automatic step-size control for linear system of equations

inferred← citeshttps://doi.org/10.1016/j.apnum.2011.11.004openalex-snapshot

Iterative refinement techniques for solving block linear systems of equations

inferred← citeshttps://doi.org/10.1016/j.parco.2016.05.014openalex-snapshot

Parallel iterative refinement linear least squares solvers based on all-reduce operations

inferred← citeshttps://doi.org/10.1016/j.parco.2020.102663openalex-snapshot

AIR: Iterative refinement acceleration using arbitrary dynamic precision

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

References

inferred← citeshttps://doi.org/10.1016/s1570-8659(00)07002-2openalex-snapshot

Gaussian elimination for the solution of linear systems of equations

inferred← citeshttps://doi.org/10.1017/cbo9781139108188openalex-snapshot

Numerical Analysis for Engineers and Scientists

inferred← citeshttps://doi.org/10.1017/s0962492922000022openalex-snapshot

Mixed precision algorithms in numerical linear algebra

inferred← citeshttps://doi.org/10.1023/a:1019137919461openalex-snapshot

Stable solution of tridiagonal systems

inferred← citeshttps://doi.org/10.1080/00207160.2010.492424openalex-snapshot

A note on Wilkinson's iterative refinement of solution with automatic step-size control

inferred← citeshttps://doi.org/10.1080/00207160701753611openalex-snapshot

Iterative refinement of computing inverse matrix

inferred← citeshttps://doi.org/10.1080/00207160802247604openalex-snapshot

Extended version with the analysis of dynamic system for iterative refinement of solution

inferred← citeshttps://doi.org/10.1090/s0025-5718-1980-0572859-4openalex-snapshot

Iterative Refinement Implies Numerical Stability for Gaussian Elimination

inferred← citeshttps://doi.org/10.1093/imanum/17.4.495openalex-snapshot

Iterative refinement for linear systems and LAPACK

inferred← citeshttps://doi.org/10.1093/oso/9780198500148.003.0001openalex-snapshot

Recent Developments in Dense Numerical Linear Algebra

inferred← citeshttps://doi.org/10.1109/12.364541openalex-snapshot

Floating point fault tolerance with backward error assertions

inferred← citeshttps://doi.org/10.1109/12.588072openalex-snapshot

Extending backward error assertions to tolerance of large errors in floating point computations

inferred← citeshttps://doi.org/10.1109/acc.1995.532688openalex-snapshot

Numerically reliable computation of characteristic polynomials

inferred← citeshttps://doi.org/10.1109/jetcas.2018.2850665openalex-snapshot

Energy-Efficient Iterative Refinement Using Dynamic Precision

inferred← citeshttps://doi.org/10.1109/saahpc.2011.19openalex-snapshot

Iterative Refinement on FPGAs

inferred← citeshttps://doi.org/10.1109/tnnls.2020.3041677openalex-snapshot

Mixed-Precision Kernel Recursive Least Squares

inferred← citeshttps://doi.org/10.1115/1.4037417openalex-snapshot

Iterative Refinement of Accelerations in Real-Time Vehicle Dynamics

inferred← citeshttps://doi.org/10.1137/0610012openalex-snapshot

Large Growth Factors in Gaussian Elimination with Pivoting

inferred← citeshttps://doi.org/10.1137/0611002openalex-snapshot

Stability Analysis of Algorithms for Solving Confluent Vandermonde-Like Systems

inferred← citeshttps://doi.org/10.1137/0719024openalex-snapshot

Use of Iterative Refinement in the Solution of Sparse Linear Systems

inferred← citeshttps://doi.org/10.1137/1.9781611971354.ch4openalex-snapshot

4. Stability of Fast Algorithms for Structured Linear Systems

inferred← citeshttps://doi.org/10.1137/17m1140819openalex-snapshot

Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions

inferred← citeshttps://doi.org/10.1137/20m1338149openalex-snapshot

Random Matrices Generating Large Growth in LU Factorization with Pivoting

inferred← citeshttps://doi.org/10.1137/22m1487709openalex-snapshot

Mixed Precision Iterative Refinement with Sparse Approximate Inverse Preconditioning

inferred← citeshttps://doi.org/10.1137/s0895479891221563openalex-snapshot

On the Stability of the Bareiss and Related Toeplitz Factorization Algorithms

inferred← citeshttps://doi.org/10.1137/s0895479895287419openalex-snapshot

Stabilizing the Generalized Schur Algorithm

inferred← citeshttps://doi.org/10.1137/s0895479899359837openalex-snapshot

Newton's Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems

inferred← citeshttps://doi.org/10.1145/322139.322148openalex-snapshot

Scaling for Numerical Stability in Gaussian Elimination

inferred← citeshttps://doi.org/10.1145/3582493openalex-snapshot

Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement

inferred← citeshttps://doi.org/10.1145/3721124openalex-snapshot

A Mixed Precision Jacobi SVD Algorithm

inferred← citeshttps://doi.org/10.15377/2409-5761.2016.03.02.1openalex-snapshot

Forward Stability of Iterative Refinement with a Relaxation for Linear Systems

inferred← citeshttps://doi.org/10.20868/upm.thesis.48853openalex-snapshot

Contributions to Topological Formulations for the Dynamic Simulation of Vehicles

inferred← citeshttps://doi.org/10.4171/069-1/1openalex-snapshot

Henryk Woźniakowski and the complexity of continuous problems

inferred← citeshttps://doi.org/10.48550/arxiv.1005.0671openalex-snapshot

Stability of fast algorithms for structured linear systems

inferred← citeshttps://doi.org/10.7916/d8kw5q2ropenalex-snapshot

The Accurate Solution of Certain Continuous Problems Using Only Single Precision

Editorial review for independent work. ICSAC — the Institute for Complexity Science and Advanced Computing — runs a structured editorial panel for researchers publishing outside journals, and publishes on CiteStamp rails. Submission is free and goes through ORCID: icsacinstitute.org/submit.