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A Useful Form of Unitary Matrix Obtained from Any Sequence of Unit 2-Norm n -Vectors

https://doi.org/10.1137/080725167
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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/bf01934122openalex-snapshot
Solving linear least squares problems by Gram-Schmidt orthogonalization
inferredcites →https://doi.org/10.1007/bf01935013openalex-snapshot
Solution of augmented linear systems using orthogonal factorizations
inferredcites →https://doi.org/10.1007/s002110100314openalex-snapshot
Scaled total least squares fundamentals
inferredcites →https://doi.org/10.1016/j.laa.2004.09.019openalex-snapshot
A new stable bidiagonal reduction algorithm
inferredcites →https://doi.org/10.1090/qam/42792openalex-snapshot
The principle of minimized iterations in the solution of the matrix eigenvalue problem
inferredcites →https://doi.org/10.1093/imanum/22.4.521openalex-snapshot
When modified Gram-Schmidt generates a well-conditioned set of vectors
inferredcites →https://doi.org/10.1137/050630416openalex-snapshot
Modified Gram-Schmidt (MGS), Least Squares, and Backward Stability of MGS-GMRES
inferredcites →https://doi.org/10.1137/0613015openalex-snapshot
Loss and Recapture of Orthogonality in the Modified Gram–Schmidt Algorithm
inferredcites →https://doi.org/10.1137/0702016openalex-snapshot
Calculating the Singular Values and Pseudo-Inverse of a Matrix
inferredcites →https://doi.org/10.1137/0712047openalex-snapshot
Solution of Sparse Indefinite Systems of Linear Equations
inferredcites →https://doi.org/10.1137/0907058openalex-snapshot
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
inferredcites →https://doi.org/10.1137/s0895479803424347openalex-snapshot
A Rank- k Update Procedure for Reorthogonalizing the Orthogonal Factor from Modified Gram--Schmidt
inferredcites →https://doi.org/10.1145/355984.355989openalex-snapshot
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
inferredcites →https://doi.org/10.1145/355993.356000openalex-snapshot
Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems
inferredcites →https://doi.org/10.6028/jres.045.026openalex-snapshot
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
inferredcites →https://doi.org/10.6028/jres.049.006openalex-snapshot
Solution of systems of linear equations by minimized iterations
inferredcites →https://doi.org/10.6028/jres.049.044openalex-snapshot
Methods of conjugate gradients for solving linear systems

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.1839openalex-snapshot
Gram‐Schmidt orthogonalization: 100 years and more
inferred← citeshttps://doi.org/10.1002/nla.2343openalex-snapshot
Low synchronization Gram–Schmidt and generalized minimal residual algorithms
inferred← citeshttps://doi.org/10.1007/978-3-030-63393-6_4openalex-snapshot
Improving the Performance of the GMRES Method Using Mixed-Precision Techniques
inferred← citeshttps://doi.org/10.1007/978-3-319-95168-3_29openalex-snapshot
The Effects of Loss of Orthogonality on Large Scale Numerical Computations
inferred← citeshttps://doi.org/10.1007/978-3-642-40020-9_88openalex-snapshot
Geometric Mean Algorithms Based on Harmonic and Arithmetic Iterations
inferred← citeshttps://doi.org/10.1007/s00211-013-0518-8openalex-snapshot
Reorthogonalization for the Golub–Kahan–Lanczos bidiagonal reduction
inferred← citeshttps://doi.org/10.1007/s10543-009-0239-7openalex-snapshot
The regularizing effect of the Golub-Kahan iterative bidiagonalization and revealing the noise level in the data
inferred← citeshttps://doi.org/10.1007/s11128-013-0588-7openalex-snapshot
The rational approximations of the unitary groups
inferred← citeshttps://doi.org/10.1016/j.cam.2024.116414openalex-snapshot
Backward error analysis of the Lanczos bidiagonalization with reorthogonalization
inferred← citeshttps://doi.org/10.1016/j.laa.2013.05.009openalex-snapshot
An augmented analysis of the perturbed two-sided Lanczos tridiagonalization process
inferred← citeshttps://doi.org/10.1016/j.laa.2020.07.024openalex-snapshot
Structure in loss of orthogonality
inferred← citeshttps://doi.org/10.1016/j.rinam.2025.100666openalex-snapshot
Lanczos algorithm explained in statistics
inferred← citeshttps://doi.org/10.1137/090761343openalex-snapshot
An Augmented Stability Result for the Lanczos Hermitian Matrix Tridiagonalization Process
inferred← citeshttps://doi.org/10.1137/100796285openalex-snapshot
Hessenberg Matrix Properties and Ritz Vectors in the Finite-Precision Lanczos Tridiagonalization Process
inferred← citeshttps://doi.org/10.1137/100799265openalex-snapshot
Restarting the Nonsymmetric Lanczos Algorithm for Eigenvalues and Linear Equations Including Multiple Right-Hand Sides
inferred← citeshttps://doi.org/10.1137/110851006openalex-snapshot
Short-Term Recurrence Krylov Subspace Methods for Nearly Hermitian Matrices
inferred← citeshttps://doi.org/10.1137/120889848openalex-snapshot
Differentiating the Method of Conjugate Gradients
inferred← citeshttps://doi.org/10.1137/120895639openalex-snapshot
Stability of Two Direct Methods for Bidiagonalization and Partial Least Squares
inferred← citeshttps://doi.org/10.1137/120897687openalex-snapshot
Properties of a Unitary Matrix Obtained from a Sequence of Normalized Vectors
inferred← citeshttps://doi.org/10.1137/15m1030078openalex-snapshot
Numerical Equivalences among Krylov Subspace Algorithms for Skew-Symmetric Matrices
inferred← citeshttps://doi.org/10.1137/17m1114363openalex-snapshot
On an Economic Arnoldi Method for $BML$-Matrices
inferred← citeshttps://doi.org/10.1137/17m1133725openalex-snapshot
Accuracy of the Lanczos Process for the Eigenproblem and Solution of Equations
inferred← citeshttps://doi.org/10.1137/18m1197400openalex-snapshot
Block Modified Gram--Schmidt Algorithms and Their Analysis
inferred← citeshttps://doi.org/10.1137/22m1519523openalex-snapshot
Analyzing Vector Orthogonalization Algorithms
inferred← citeshttps://doi.org/10.1137/22m1541083openalex-snapshot
The Joint Bidiagonalization of a Matrix Pair with Inaccurate Inner Iterations
inferred← citeshttps://doi.org/10.1137/23m1585817openalex-snapshot
Probabilistic Rounding Error Analysis of Modified Gram–Schmidt
inferred← citeshttps://doi.org/10.1137/24m1655482openalex-snapshot
Rounding Error Analysis of the Inverse Compact WY Modified Gram–Schmidt Algorithms
inferred← citeshttps://doi.org/10.1177/10943420251382476openalex-snapshot
HPL-MxP benchmark: Mixed-precision algorithms, iterative refinement, and scalable data generation
inferred← citeshttps://doi.org/10.48550/arxiv.1907.10550openalex-snapshot
Exploiting variable precision in GMRES
inferred← citeshttps://doi.org/10.48550/arxiv.2008.05358openalex-snapshot
On inner iterations of the joint bidiagonalization based algorithms for solving large scale ill-posed problems
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