Abstract

The generalized Schur algorithm is a powerful tool allowing to compute classicaldecompositions of matrices, such as the QR and LU factorizations. When applied to matrices withparticular structures, the generalized Schur algorithm computes these factorizations with a complexityof one order of magnitude less than that of classical algorithms based on Householder or elementarytransformations. In this manuscript, we describe the main features of the generalized Schur algorithm.We show that it helps to prove some theoretical properties of the R factor of the QR factorization ofsome structured matrices, such as symmetric positive definite Toeplitz and Sylvester matrices, thatcan hardly be proven using classical linear algebra tools. Moreover, we propose a fast implementationof the generalized Schur algorithm for computing the rank of Sylvester matrices, arising in a numberof applications. Finally, we propose a generalized Schur based algorithm for computing the -spaceof polynomial matrices.

Autore Pugliese

• Mastronardi Nicola , Laudadio Teresa

Tutti gli autori

• Laudadio T.; Mastronardi N.; Van Dooren P.

Titolo volume/Rivista

Axioms

Anno di pubblicazione

2018

ISSN

2075-1680

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

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Numero di citazioni Scopus

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Ultimo Aggiornamento Citazioni

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Settori ERC

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Codici ASJC

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