Based on [4], we prove a variation of the theorem in title, for equations with periodic coefficients, in Fréchet spaces. The main result gives equivalent conditions ensuring the reduction of such an equation to one with constant coefficient. In the particular case of C ∞ , we obtain the exact analogue of the classical theorem. Our approach essentially uses the fact that a Fréchet space is the l...

The nonlinear Diffuse Optical Tomography (DOT) problem involves the inversion of the associated coefficient-to-measurement operator, which maps the spatially varying optical coefficients of turbid medium to the boundary measurements. The inversion of the coefficient-to-measurement operator is approximated by using the Fréchet derivative of the operator. In this work, we first analyze the Born e...

A new methodology leading to the construction of a universal connection for Fréchet principal bundles is proposed in this paper. The classical theory, applied successfully so far for finite dimensional and Banach modelled bundles, collapses within the framework of Fréchet manifolds. However, based on the replacement of the space of continuous linear mappings by an appropriate topological vector...

Based on the methods from interpolation theory we give a characterization of pairs (E,F ) of Fréchet-Hilbert spaces so that for each Fréchet-Hilbert space G each short exact sequence 0 −→ F −→ G −→ E −→ 0 splits. This characterization essentially depends on a key condition (S) of an interpolation nature. An equivalent description of (S) in terms of appropriate families of interpolation function...

Abstract.— We describe the use of the Fréchet mean and variance in the Billera-Holmes-Vogtmann (BHV) treespace to summarize and explore the diversity of a set of phylogenetic trees. We show that the Fréchet mean is comparable to other summary methods, despite its stickiness property, and that the Fréchet variance is faster and more precise than commonly used variance measures. These mean and va...

We revisit the problem of computing the Fréchet distance between polygonal curves, focusing on the discrete Fréchet distance, where only distance between vertices is considered. We develop efficient approximation algorithms for two natural classes of curves: κ-bounded curves and backbone curves, the latter of which are widely used to model molecular structures. We also propose a pseudo–output-s...

In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [21], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (Dp,Wp), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fréchet mean of a f...

HIGHER ORDER FRÉCHET DERIVATIVES OF MATRIX FUNCTIONS AND THE LEVEL-2 CONDITION NUMBER∗ NICHOLAS J. HIGHAM† AND SAMUEL D. RELTON† Abstract. The Fréchet derivative Lf of a matrix function f : C n×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 to higher ord...

The Fréchet distance is a popular and widespread distance measure for point sequences and for curves. About two years ago, Agarwal et al [SIAM J. Comput. 2014] presented a new (mildly) subquadratic algorithm for the discrete version of the problem. This spawned a flurry of activity that has led to several new algorithms and lower bounds. In this paper, we study the approximability of the discre...

Resumen. En este artículo desarrollamos una teoría general de convergencia de un método secante para resolver ecuaciones matriciales no lineales. Además, presentamos condiciones suficientes para que este método proporcione un algoritmo local y superlinealmente convergente. Palabras clave: Función matricial, operador de Fréchet, Fréchet diferenciable, método secante, ecuación matricial no lineal...