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Advanced Numerical Methods in Applied Sciences

The generalized Schur algorithm (GSA) allows computing well-known matrix decompositions,
such as QR and LU factorizations [1]. In particular, if the involved matrix is structured, i.e., Toeplitz, block-Toeplitz or Sylvester, the GSA computes the R factor of the QR factorization with complexity of one order of magnitude less than that of the classical QR algorithm [2], since it relies only on the knowledge of the so-called generators [2] associated to the given matrix, rather than on the knowledge of the matrix itself. The stability properties of the GSA are described in [3–5], where it is proven that the algorithm is weakly stable provided the involved hyperbolic rotations are performed in a stable way. In this manuscript, we first show that, besides the efficiency properties, the GSA provides new theoretical insights on the bounds of the entries of the R factor of the QR factorization of some structured matrices

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Series Title
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Call Number
510 ADV
Publisher
Basel : MDPI - Multidisciplinary Digital Publishing Institute.,
Collation
-
Language
English
ISBN/ISSN
978-3-03897-667-7
Classification
510
Content Type
text
Media Type
computer
Carrier Type
online resource
Edition
-
Subject(s)
Numerical Methods
Specific Detail Info
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Statement of Responsibility
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Khusnun
Source
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Validator
maya
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