On theoretical and numerical aspects of symplectic Gram?Schmidt-like algorithms

A. Salam

Type: Article

Publication Date: 2005-04-06

Citations: 27

DOI: https://doi.org/10.1007/s11075-005-0963-2

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Numerical Algorithms - View

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+ PDF Chat	A treatment of breakdowns and near breakdowns in a reduction of a matrix to upper <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e19" altimg="si11.gif"><mml:mi>J</mml:mi></mml:math>-Hessenberg form and related topics	2019	A. Salam Haïthem Ben Kahla
+	Symplectic Gram-Schmidt Algorithm with Re-Orthogonalization	2011	Eman Salem Alaidarous
+	Optimal symplectic Householder transformations for SR decomposition	2008	A. Salam Eman Salem Alaidarous A. El Farouk
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+ PDF Chat	Optimization on the symplectic Stiefel manifold: SR decomposition-based retraction and applications	2023	Bin Gao Nguyen Thanh Son Tatjana Stykel
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+	Structure-preserving reduced basis methods for Poisson systems	2020	Jan S. Hesthaven Cecilia Pagliantini
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Works Cited by This (18)

Action	Title	Year	Authors
+	A MULTISHIFT ALGORITHM FOR THE NUMERICAL SOLUTION OF ALGEBRAIC RICCATI EQUATIONS	1993	Gregory Ammar Peter Benner Volker Mehrmann
+	Cholesky-like Factorizations of Skew-Symmetric Matrices	2000	Peter Benner Ralph Byers Heike Faßbender Volker Mehrmann David S. Watkins
+	Algebraic Riccati Equations	2006	Peter Lancaster Leiba Rodman
+	A symplectic QR like algorithm for the solution of the real algebraic Riccati equation	1986	Angelika Bunse‐Gerstner Volker Mehrmann
+	Solving linear least squares problems by Gram-Schmidt orthogonalization	1967	Åke Björck
+	An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem	1997	Peter Benner Heike Faβbender
+	Structure-Preserving Methods for Computing Eigenpairs of Large Sparse Skew-Hamiltonian/Hamiltonian Pencils	2001	Volker Mehrmann David S. Watkins
+	Canonical forms for symplectic and Hamiltonian matrices	1974	Alan J. Laub Kenneth R. Meyer
+	A Hamiltonian $QR$ Algorithm	1986	Ralph Byers
+	Matrix factorizations for symplectic QR-like methods	1986	Angelika Bunse‐Gerstner