Computing the fréchet derivative of the matrix logarithm and estimating the condition number [PDF]
, 2012 The most popular method for computing the matrix logarithm is the inverse scaling and squaring method, which is the basis of the recent algorithm of Al-Mohy and Higham [SIAM J. Sci. Comput., 34 (2012), pp. C152-C169].
Higham, Nicholas J. +5 more
core +1 more source
Ball convergence for Traub-Steffensen like methods in Banach space
Annals of the West University of Timisoara: Mathematics and Computer Science, 2015 We present a local convergence analysis for two Traub-Steffensen-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. In earlier studies such as [16, 23] Taylor expansions and hypotheses up to the third
Argyros Ioannis K., George Santhosh
doaj +1 more source
A global sensitivity index based on Fréchet derivative and its efficient numerical analysis [PDF]
, 2020 Sensitivity analysis plays an important role in reliability evaluation, structural optimization and structural design, etc. The local sensitivity, i.e., the partial derivative of the quantity of interest in terms of parameters or basic variables, is ...
Beer, Michael +2 more
core +1 more source
ON THE FRECHET DIFFERENTIABILITY OF LUXEMBURG NORM IN THE SEQUENCE SPACES l^{p_n} WITH VARIABLE EXPONENTS [PDF]
Romanian Journal of Mathematics and Computer Science, 2014 It is shown that the Luxemburg norm in the sequence space l^{(p_n)} with variable exponents is Frechet - differentiable and a formula expressing the Frechet derivative of this norm at any nonzero x ∈ l^{(p_n)} is given.
PAVEL MATEI
doaj
Mathematical Determination of the Fréchet Derivative with Respect to the Domain for a Fluid-Structure Scattering Problem. Case of Polygonal-Shaped Domains [PDF]
, 2017 International audienceThe characterization of the Fréchet derivative of the elasto-acoustic scattered field with respect to Lipschitz continuous polygonal domains is established.
Djellouli, Rabia +3 more
core +4 more sources
Semilocal Convergence of the Extension of Chun’s Method
Axioms, 2021 In this work, we use the technique of recurrence relations to prove the semilocal convergence in Banach spaces of the multidimensional extension of Chun’s iterative method.
Alicia Cordero +4 more
doaj +1 more source
On the Fréchet derivative of matrix functions
, 1987 In 1956 Rinehart [4] discussed the derivatives of matrix functions by considering differences ƒ(A + E) − ƒ(A) for matrices E commuting with A. In that case the derivative turned out to be ƒ′(A). In this paper the case of noncommutative A and E is treated.
Stickel, Eberhard
core +1 more source
The Newton's method for operators with Hölder continuous ffrst derivative. [PDF]
, 2001 We analyze the convergence of the Newton method when the first Fréchet derivative of the operator involved is Hölder continuous. We calculate also the R-order of convergence and provide some a priori error bounds.
Hernández, M.A. [0000-0001-5478-2958]
core +1 more source
Calculus for linearly correlated fuzzy function using fréchet derivative and riemann integral
, 2020 In this manuscript we study integration and derivative theories for interactive fuzzy processes. These theories are based on the Fréchet derivative and the Riemann integral.
Barros, Laécio Carvalho de +2 more
core +1 more source
The complex step approximation to the fréchet derivative of a matrix function [PDF]
, 2009 We show that the Fréchet derivative of a matrix function f at A in the direction E, where A and E are real matrices, can be approximated by Im f(A + ihE)/h for some suitably small h. This approximation, requiring a single function evaluation at a complex
Higham, Nicholas J., Al-Mohy, Awad H.
core +1 more source