Volume 39, pp. 414-436, 2012.
Computation of the matrix $p$th root and its Fréchet derivative by integrals
João R. Cardoso
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.
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matrix $p$th root, Fréchet derivative, quadrature, composite trapezoidal rule, Gauss-Legendre rule, adaptive Simpson rule
AMS subject classifications
Links to the cited ETNA articles
|||Vol. 38 (2011), pp. 202-217 João R. Cardoso: Evaluating the Fréchet derivative of the matrix pth root|