Geodesic
Computation of the matrix $p$th root and its Fréchet derivative by integrals
Electronic transactions on numerical analysis, Tome 39 (2012), pp. 414-436.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We present new integral representations for the matrix $p$th root and its Fréchet derivative and then investigate the computation of these functions by numerical quadrature. Three different quadrature rules are considered: composite trapezoidal, Gauss-Legendre and adaptive Simpson. The problem of computing the matrix $p$th root times a vector without the explicit evaluation of the $p$th root is also analyzed and bounds for the norm of the matrix $p$th root and its Fréchet derivative are derived.
Classification : 65F60, 65D30
Keywords: matrix $p$th root, Fréchet derivative, quadrature, composite trapezoidal rule, Gauss-Legendre rule, adaptive simpson rule 
@article{ETNA_2012__39__a2,
     author = {Cardoso, Jo\~ao R.},
     title = {Computation of the matrix $p$th root and its {Fr\'echet} derivative by integrals},
     journal = {Electronic transactions on numerical analysis},
     pages = {414--436},
     publisher = {mathdoc},
     volume = {39},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2012__39__a2/}
}
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Cardoso, João R. Computation of the matrix $p$th root and its Fréchet derivative by integrals. Electronic transactions on numerical analysis, Tome 39 (2012), pp. 414-436. http://geodesic.mathdoc.fr/item/ETNA_2012__39__a2/