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Alicja Smoktunowicz
Researcher at Warsaw University of Technology
Publications - 36
Citations - 287
Alicja Smoktunowicz is an academic researcher from Warsaw University of Technology. The author has contributed to research in topics: Numerical stability & Condition number. The author has an hindex of 9, co-authored 33 publications receiving 227 citations.
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Set-theoretic solutions of the Yang–Baxter equation and new classes of R-matrices
TL;DR: In this paper, a correspondence between one-generator braces and indecomposable, non-degenerate set-theoretic solutions of the quantum Yang-Baxter equation is established.
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A note on the error analysis of classical Gram–Schmidt
TL;DR: The work presented here shows that the computed R satisfies RT R = AT A + E where E is an appropriately small backward error, but only if the diagonals of R are computed in a manner similar to Cholesky factorization of the normal equations matrix.
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Numerical stability of orthogonalization methods with a non-standard inner product
TL;DR: This paper studies the numerical properties of several orthogonalization schemes where the inner product is induced by a nontrivial symmetric and positive definite matrix and considers the implementation based on the backward stable eigendecomposition, modified and classical Gram–Schmidt algorithms, Gram-Schmidt process with reorthogonalized as well as the implementation motivated by the AINV approximate inverse preconditioner.
Posted Content
Reorthogonalized Block Classical Gram--Schmidt
TL;DR: In this article, a reorthogonalized block classical Gram-Schmidt algorithm is proposed that factorizes a full column rank matrix $A$ into $A=QR$ where $Q$ is left orthogonal (has orthonormal columns) and $R$ is upper triangular and nonsingular.
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Backward Stability of Clenshaw's Algorithm
TL;DR: In this paper, the authors study numerical properties of Clenshaw's algorithm for summing the series w = ∑n = 0Nbnpn where pn satisfies the linear three-term recurrence relation.