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Iterative refinement enhances the stability ofQR factorization methods for solving linear equations
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1007/978-1-4613-0535-4_4openalex-snapshot
A Project for Developing a Linear Algebra Library for High-Performance Computers
inferredcites →https://doi.org/10.1007/bf01386090openalex-snapshot
Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
inferredcites →https://doi.org/10.1007/bf01389335openalex-snapshot
On the augmented system approach to sparse least-squares problems
inferredcites →https://doi.org/10.1007/bf01436299openalex-snapshot
Algorithms for confluent Vandermonde systems
inferredcites →https://doi.org/10.1007/bf01931284openalex-snapshot
Component-wise perturbation analysis and error bounds for linear least squares solutions
inferredcites →https://doi.org/10.1007/bf01932150openalex-snapshot
Iterative refinement implies numerical stability
inferredcites →https://doi.org/10.1007/bf01939321openalex-snapshot
Iterative refinement of linear least squares solutions I
inferredcites →https://doi.org/10.1007/bf01939974openalex-snapshot
Iterative refinement of linear least squares solutions II
inferredcites →https://doi.org/10.1016/0016-0032(64)90390-4openalex-snapshot
Rounding errors in algebraic processes
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Stability analysis of the method of seminormal equations for linear least squares problems
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Comment on the Iterative Refinement of Least-Squares Solutions
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Computing error bounds for regression problems
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An Algorithm for Summing Orthogonal Polynomial Series and their Derivatives with Applications to Curve-Fitting and Interpolation
inferredcites →https://doi.org/10.1090/s0025-5718-1970-0290541-1openalex-snapshot
Solution of Vandermonde Systems of Equations
inferredcites →https://doi.org/10.1090/s0025-5718-1980-0572859-4openalex-snapshot
Iterative Refinement Implies Numerical Stability for Gaussian Elimination
inferredcites →https://doi.org/10.1093/imamat/20.3.379openalex-snapshot
An Error Analysis of the Modified Clenshaw Method for Evaluating Chebyshev and Fourier Series
inferredcites →https://doi.org/10.1093/imanum/8.4.473openalex-snapshot
Fast Solution of Vandermonde-Like Systems Involving Orthogonal Polynomials
inferredcites →https://doi.org/10.1093/oso/9780198535645.003.0016openalex-snapshot
Iterative refinement and reliable computing
inferredcites →https://doi.org/10.1137/0610013openalex-snapshot
Solving Sparse Linear Systems with Sparse Backward Error
inferredcites →https://doi.org/10.1137/0611002openalex-snapshot
Stability Analysis of Algorithms for Solving Confluent Vandermonde-Like Systems
inferredcites →https://doi.org/10.1137/0611023openalex-snapshot
Average-Case Stability of Gaussian Elimination
inferredcites →https://doi.org/10.1137/0613014openalex-snapshot
Backward Error and Condition of Structured Linear Systems
inferredcites →https://doi.org/10.1137/0722051openalex-snapshot
On the Method of Weighting for Equality-Constrained Least-Squares Problems
inferredcites →https://doi.org/10.1137/1.9781611971217openalex-snapshot
Solving Least Squares Problems
inferredcites →https://doi.org/10.1145/321386.321394openalex-snapshot
Iterative Refinement in Floating Point
inferredcites →https://doi.org/10.1145/322139.322148openalex-snapshot
Scaling for Numerical Stability in Gaussian Elimination
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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A parallel multisplitting solution of the least squares problem
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Stability of block LU factorization
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A new iterative refinement with roundoff error analysis
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Componentwise Error Analysis for Stationary Iterative Methods
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The Design of Fast and Energy-Efficient Linear Solvers: On the Potential of Half-Precision Arithmetic and Iterative Refinement Techniques
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Algorithms for Linear Least Squares Problems
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Component-wise perturbation analysis and error bounds for linear least squares solutions
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A Cholesky dual method for proximal piecewise linear programming
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Linear least squares problems with data over incomplete grids
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Acceleration of iterative refinement for singular value decomposition
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Perturbation analysis of the canonical correlations of matrix pairs
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Wilkinson’s iterative refinement of solution with automatic step-size control for linear system of equations
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An exponential approach to highly ill-conditioned linear systems
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Iterative refinement techniques for solving block linear systems of equations
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Efficient and error minimized coupling procedures for unstructured and moving meshes
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Mixed precision algorithms in numerical linear algebra
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A QR Decomposition for Matrix Pencils
inferred← citeshttps://doi.org/10.1080/00207160.2010.492424openalex-snapshot
A note on Wilkinson's iterative refinement of solution with automatic step-size control
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Extended version with the analysis of dynamic system for iterative refinement of solution
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A survey of componentwise perturbation theory in numerical linear algebra
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Iterative refinement for linear systems and LAPACK
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Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems
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Floating point fault tolerance with backward error assertions
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Extending backward error assertions to tolerance of large errors in floating point computations
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The Role of Precision for Iterative Refinement
inferred← citeshttps://doi.org/10.1109/sc.2018.00050openalex-snapshot
Harnessing GPU Tensor Cores for Fast FP16 Arithmetic to Speed up Mixed-Precision Iterative Refinement Solvers
inferred← citeshttps://doi.org/10.1137/0614001openalex-snapshot
Improved Error Bounds for Underdetermined System Solvers
inferred← citeshttps://doi.org/10.1137/0614076openalex-snapshot
A Componentwise Perturbation Analysis of the $QR$ Decomposition
inferred← citeshttps://doi.org/10.1137/0916025openalex-snapshot
Stability of Parallel Triangular System Solvers
inferred← citeshttps://doi.org/10.1137/0916056openalex-snapshot
The Instability of Parallel Prefix Matrix Multiplication
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Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions
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Three-Precision GMRES-Based Iterative Refinement for Least Squares Problems
inferred← citeshttps://doi.org/10.1137/s089547989324416xopenalex-snapshot
Fast Solution of Confluent Vandermonde Linear Systems
inferred← citeshttps://doi.org/10.1137/s0895479893246029openalex-snapshot
Backward Error Analysis for the Constrained and Weighted Linear Least Squares Problem When Using the Weighted $QR$ Factorization
inferred← citeshttps://doi.org/10.1137/s0895479893257444openalex-snapshot
Fast Algorithms for Confluent Vandermonde Linear Systems and Generalized Trummer’s Problem
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Solution of Vandermonde-Like Systems and Confluent Vandermonde-Like Systems
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A Generalized Hilbert Matrix Problem and Confluent Chebyshev--Vandermonde Systems
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Statistical Condition Estimation for Linear Systems
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Stability of block algorithms with fast level-3 BLAS
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Forward Stability of Iterative Refinement with a Relaxation for Linear Systems
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RESIDUAL-ANGLE-CONTROLLED PRECISION-SELECTIVE GMRES ITERATIVE REFINEMENT FOR ILL-CONDITIONED NONSYMMETRIC LINEAR SYSTEMS
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Incremental Learning for Online Data Using QR Factorization on Convolutional Neural Networks
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