80 research outputs found
Convergence and Asymptotic of Multi-Level Hermite-Padé Polynomials
Mención Internacional en el título de doctorPrograma de Doctorado en Ingeniería Matemática por la Universidad Carlos III de MadridPresidente: Francisco José Marcellán Español.- Secretario: Bernardo de la Calle Ysern.- Vocal: Arnoldus Bernardus Jacobus Kuijla
Systems of Markov type functions: normality and convergence of Hermite-Padé approximants
This thesis deals with Hermite-Padé approximation of analytic and merophorphic
functions. As such it is embeded in the theory of vector rational approximation of
analytic functions which in turn is intimately connectd with the theory of multiple
orthogonal polynomials. All the basic concepts and results used in this thesis involving
complex analysis and measure theory may found in classical textbooks...........Programa Oficial de Doctorado en Ingeniería MatemáticaPresidente: Francisco José Marcellán Español; Vocal: Alexander Ivanovich Aptekarev; Secretario: Andrei Martínez Finkelshtei
Center manifold and multivariable approximants applied to non-linear stability analysis
This paper presents a research devoted to the study of instability phenomena
in non-linear model with a constant brake friction coefficient. This paper
outlines the stability analysis and a procedure to reduce and simplify the
non-linear system, in order to obtain limit cycle amplitudes. The center
manifold approach, the multivariable approximants theory, and the alternate
frequency/time domain (AFT) method are applied. Brake vibrations, and more
specifically heavy trucks grabbing are concerned. The modelling introduces
sprag-slip mechanism based on dynamic coupling due to buttressing. The
non-linearity is expressed as a polynomial with quadratic and cubic terms. This
model does not require the use of brake negative coefficient, in order to
predict the instability phenomena. Finally, the center manifold approach, the
multivariable approximants, and the AFT method are used in order to obtain
equations for the limit cycle amplitudes. These methods allow the reduction of
the number of equations of the original system in order to obtain a simplified
system, without loosing the dynamics of the original system, as well as the
contributions of non-linear terms. The goal is the validation of this procedure
for a complex non-linear model by comparing results obtained by solving the
full system and by using these methods. The brake friction coefficient is used
as an unfolding parameter of the fundamental Hopf bifurcation point
Coarse-graining Kohn-Sham Density Functional Theory
We present a real-space formulation for coarse-graining Kohn-Sham Density
Functional Theory that significantly speeds up the analysis of material defects
without appreciable loss of accuracy. The approximation scheme consists of two
steps. First, we develop a linear-scaling method that enables the direct
evaluation of the electron density without the need to evaluate individual
orbitals. We achieve this by performing Gauss quadrature over the spectrum of
the linearized Hamiltonian operator appearing in each iteration of the
self-consistent field method. Building on the linear-scaling method, we
introduce a spatial approximation scheme resulting in a coarse-grained Density
Functional Theory. The spatial approximation is adapted so as to furnish fine
resolution where necessary and to coarsen elsewhere. This coarse-graining step
enables the analysis of defects at a fraction of the original computational
cost, without any significant loss of accuracy. Furthermore, we show that the
coarse-grained solutions are convergent with respect to the spatial
approximation. We illustrate the scope, versatility, efficiency and accuracy of
the scheme by means of selected examples
Pade Approximants And One Of Its Applications
This thesis is concerned with a brief summary of the theory of Pade approximants and one of its applications to Finance. Proofs of most of the theorems are omitted and many developments could not be mentioned due to the vastness of the field of Pade approximations. We provide reference to research papers and books that contain exhaustive treatment of the subject. This thesis is mainly divided into two parts. In the first part we derive a general expression of the Pade approximants and some of the results that will be related to the work on the second part of the thesis. The Aitken\u27s method for quick convergence of series is highlighted as Pade[L/1] . We explore the criteria for convergence of a series approximated by Pade approximants and obtain its relationship to numerical analysis with the help of the Crank-Nicholson method. The second part shows how Pade approximants can be a smooth method to model the term structure of interest rates using stochastic processes and the no arbitrage argument. Pade approximants have been considered by physicists to be appropriate for approximating large classes of functions. This fact is used here to compare Pade approximants with very low indices and two parameters to interest rates variations provided by the Federal Reserve System in the United States
- …