The tensor t-function, a formalism that generalizes the well-known concept of matrix functions to third-order tensors, is introduced in [K. Lund, t-function: definition for Numer. Linear Algebra Appl. 27 (3), e2288]. In this work, we investigate properties Fr\'echet derivative t-function and derive algorithms its efficient numerical computation. Applications condition number estimation nuclear ...

in this paper, simultaneous control of source terms is considered in a vibrational string problem.in the considered problem, the terms to be controlled are the force and the initial velocity functions. we statethe generalized (weak) solution about the considered problem. the existence and uniqueness of the solutionfor optimal control problem is investigated. the frechet derivative of the functi...

We propose an improved fast local level set method for the inverse problem of gravimetry by developing two novel algorithms: one is of linear complexity designed for computing the Frechet derivative of the nonlinear domain inverse problem, and the other is designed for carrying out numerical continuation rapidly so as to obtain fictitious full measurement data from partial measurement. Since th...

"In this paper we investigate the existence of solutions initial value problems (IVP for short), partial hyperbolic functional and neutral differential inclusions fractional order involving Caputo derivative with finite delay by using nonlinear alternative Frigon type multivalued admissible contraction in Frechet spaces."

Some basic concepts for functions defined on subsets of the unit sphere, such as s-directional derivative, s-gradient and s-Gateaux s-Frechet differentiability etc, are introduced investigated. These different from usual ones Euclidean spaces, however, results obtained here very similar. Then, applications, we provide some criterions s-convexity spheres which improvements or refinements known r...

The modification of the Clarke generalized subdiNerentia1 due to Michel and Penot is a useful tool in determining differentiability properties for certain classes of real functions on a normed linear space. The Glteaux differentiability of any real function can be deduced from the GBteaux differentiability of the norm if the function has a directional derivative which attains a constant related...

S U M M A R Y We present an alternative to the classical mode coupling method scheme often used in global seismology to compute synthetic seismograms in laterally heterogeneous earth model and Frechet derivatives for tomographic inverse problem with the normal modes first-order Born approximation. We start from the first-order Born solution in the frequency domain and we use a numerical scheme ...

In this study, we consider an optimal control problem for Euler-Bernoulli beam equation. The initial velocity of the system is given by function. We give sufficient conditions existence a unique solution hyperbolic and prove that considered exists unique. After obtaining Frechet derivative cost functional via adjoint problem, also iteration algorithm numerical using Gradient method. Finally, fu...

Summary This paper formalizes in Mizar [1], [2], that the isometric isomorphisms between spaces formed by an ( n + 1)-dimensional multilinear map and -fold composition of linear maps on real normed spaces. result is used to describe space nth-order derivatives Frechet derivative as a space. In Section 1, we discuss 1-dimensional 0-fold compositions preparation, 2, extend discussion compositions...