Advanced Numerical Methods in Applied Sciences

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Title

Advanced Numerical Methods in Applied Sciences

Subject

Numerical Methods

Description

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

Creator

Brugnano, Luigi, - Iavernaro, Felice

Source

https://www.mdpi.com/books/pdfview/book/1360

Publisher

MDPI - Multidisciplinary Digital Publishing Institute

Date

2019

Contributor

Baihaqi

Rights

Creative Commons

Format

Ebooks

Language

English

Type

Textbooks

Files

Citation

Brugnano, Luigi, - Iavernaro, Felice , “Advanced Numerical Methods in Applied Sciences,” Open Educational Resource (OER) - Unsyiah Library, accessed January 28, 2023, http://uilis.unsyiah.ac.id/oer/items/show/2965.

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