scholarly journals A Block Krylov Method to Compute the Action of the Fréchet Derivative of a Matrix Function on a Vector with Applications to Condition Number Estimation

2017 ◽  
Vol 39 (4) ◽  
pp. A1416-A1434 ◽  
Author(s):  
Peter Kandolf ◽  
Samuel D. Relton
Keyword(s):  
Condition Number ◽  
Matrix Function ◽  
Fréchet Derivative ◽  
Frechet Derivative ◽  
Krylov Method

scholarly journals Computing the Fréchet Derivative of the Matrix Logarithm and Estimating the Condition Number

2013 ◽  
Vol 35 (4) ◽  
pp. C394-C410 ◽  
Author(s):  
Awad H. Al-Mohy ◽  
Nicholas J. Higham ◽  
Samuel D. Relton
Keyword(s):  
Condition Number ◽  
Fréchet Derivative ◽  
Frechet Derivative ◽  
Matrix Logarithm ◽  
The Matrix

scholarly journals A gradient technique for an optimal control problem governed by a system of nonlinear first order partial differential equations

1995 ◽  
Vol 36 (3) ◽  
pp. 261-273 ◽  
Author(s):  
Mohammad A. Kazemi
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Problems ◽  
Fréchet Derivative ◽  
Necessary Condition ◽  
Control Problems ◽  
Partial Differential ◽  
Frechet Derivative ◽  
First Order

AbstractIn this paper a class of optimal control problems with distributed parameters is considered. The governing equations are nonlinear first order partial differential equations that arise in the study of heterogeneous reactors and control of chemical processes. The main focus of the present paper is the mathematical theory underlying the algorithm. A conditional gradient method is used to devise an algorithm for solving such optimal control problems. A formula for the Fréchet derivative of the objective function is obtained, and its properties are studied. A necessary condition for optimality in terms of the Fréchet derivative is presented, and then it is shown that any accumulation point of the sequence of admissible controls generated by the algorithm satisfies this necessary condition for optimality.

On the non-reducibility of the (u,v)-derivative to the Fréchet derivative

1982 ◽  
Vol 37 (1) ◽  
pp. 153-154
Author(s):  
I A Bakhtin ◽  
V I Sobolev ◽  
V M Shcherbin
Keyword(s):  
Fréchet Derivative ◽  
Frechet Derivative
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