Results 41 to 50 of about 345,162 (102)
, 2013 International audienceWe establish the continuous Fréchet differentiability of the elasto-acoustic field with respect to Lipschitz continuous deformation of the shape of an elastic scatterer.
Djellouli, Rabia +2 more
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Higher order fréchet derivatives of matrix functions and the level-2 condition number [PDF]
, 2013 © 2014 SIAM.The Fréchet derivative Lf of a matrix function f: ℂn×n → ℂn×n controls the sensitivity of the function to small perturbations in the matrix. While much is known about the properties of Lf and how to compute it, little attention has been given
Higham, Nicholas J., Relton, Samuel D.
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Fréchet differentiability of the solutions of a semilinear abstract Cauchy problem [PDF]
, 2005 Sufficient conditions are found under which the solutions z(t;q) of a semilinear abstract Cauchy problem of the form ddtz(t)=A(q)z(t)+F(q,t,z(t)) are Fréchet differentiable with respect to the parameter q. An explicit form is provided for the sensitivity
Terry Herdman +3 more
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On the Numerical Solution of a Hyperbolic Inverse Boundary Value Problem in Bounded Domains
Mathematics, 2022 We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation.
Roman Chapko, Leonidas Mindrinos
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Local convergence of the Gauss-Newton-Kurchatov method under generalized Lipschitz conditions
Karpatsʹkì Matematičnì Publìkacìï, 2021 We investigate the local convergence of the Gauss-Newton-Kurchatov method for solving nonlinear least squares problems. This method is a combination of Gauss-Newton and Kurchatov methods and it is used for problems with the decomposition of the operator.
S.M. Shakhno, H.P. Yarmola
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Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2017 This paper is devoted to the study of a multi-step method with divided differences for solving nonlinear equations in Banach spaces. In earlier studies, hypotheses on the Fréchet derivative up to the sixth order of the operator under consideration is ...
Ioannis K. Argyros, Santhosh George
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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
Higham, Nicholas J., Al-Mohy, Awad H.
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Extending the Applicability of Stirling’s Method
Mathematics, 2019 Stirling’s method is considered as an alternative to Newton’s method when the latter fails to converge to a solution of a nonlinear equation.
Cristina Amorós +5 more
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Convergence Analysis and Dynamical Nature of an Efficient Iterative Method in Banach Spaces
Mathematics, 2021 We study the local convergence analysis of a fifth order method and its multi-step version in Banach spaces. The hypotheses used are based on the first Fréchet-derivative only. The new approach provides a computable radius of convergence, error bounds on
Deepak Kumar +3 more
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Computing the fréchet derivative of the matrix exponential, with an application to condition number estimation [PDF]
, 2008 The matrix exponential is a much-studied matrix function having many applications. The Fréchet derivative of the matrix exponential describes the first-order sensitivity of eA to perturbations in A and its norm determines a condition number for eA. Among
Higham, Nicholas J. +3 more
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