Iterative methods for solving nonlinear least squares problems

Iterative methods for solving nonlinear least squares problem

On the construction of discrete approximations to linear differential expressions

Algorithm for generating discrete approximations in terms of ordinates for linear differential expression

Difference Methods and Deferred Corrections for Ordinary Boundary Value Problems

Compact as possible difference schemes for systems of nth order equations are developed. Generalizations of the Mehrstellenverfahren and simple theoretically sound implementations of deferred corrections are given. It is shown that higher order systems are more efficiently solved as given rather than as reduced to larger lower order systems. Tables of coefficients to implement these methods are included and have been derived using symbolic computations

Dissociative Adsorption: A Solvable Model

A model of "hot"-dimer deposition in one dimension, introduced by Pereyra and Albano, is modified to have an unbounded dissociation range. The resulting dynamical equations are solved exactly. A related k-mer dissociation model is also introduced and its solution obtained as a quadrature.Comment: TeX (plain

On the non-convergence of the Wang-Landau algorithms with multiple random walkers

This paper discusses some convergence properties in the entropic sampling Monte Carlo methods with multiple random walkers, particularly in the Wang-Landau (WL) and $1/t$ algorithms. The classical algorithms are modified by the use of $m$ independent random walkers in the energy landscape to calculate the density of states (DOS). The Ising model is used to show the convergence properties in the calculation of the DOS, as well as the critical temperature, while the calculation of the number $\pi$ by multiple dimensional integration is used in the continuum approximation. In each case, the error is obtained separately for each walker at a fixed time, $t$; then, the average over $m$ walkers is performed. It is observed that the error goes as $1/\sqrt{m}$. However, if the number of walkers increases above a certain critical value $m>m_x$, the error reaches a constant value (i.e. it saturates). This occurs for both algorithms; however, it is shown that for a given system, the $1/t$ algorithm is more efficient and accurate than the similar version of the WL algorithm. It follows that it makes no sense to increase the number of walkers above a critical value $m_x$, since it does not reduces the error in the calculation. Therefore, the number of walkers does not guarantee convergence.Comment: 10 pages, 12 figures, Regular Articl

Computation of the pseudinverse of a matrix of unknown rank

Least squares solution to linear system and computation of pseudoinverse by matrix of unknown ran

Optical polarimetric monitoring of the type II-plateau SN 2005af

Aims. Core-collapse supernovae may show significant polarization that implies non-spherically symmetric explosions. We observed the type II-plateau SN 2005af using optical polarimetry in order to verify whether any asphericity is present in the supernova temporal evolution. Methods. We used the IAGPOL imaging polarimeter to obtain optical linear polarization measurements in R (five epochs) and V (one epoch) broadbands. Interstellar polarization was estimated from the field stars in the CCD frames. The optical polarimetric monitoring began around one month after the explosion and lasted ~30 days, between the plateau and the early nebular phase. Results. The weighted mean observed polarization in R band was [1.89 +/- 0.03]% at position angle (PA) 54 deg. After foreground subtraction, the level of the average intrinsic polarization for SN 2005af was ~0.5% with a slight enhancement during the plateau phase and a decline at early nebular phase. A rotation in PA on a time scale of days was also observed. The polarimetric evolution of SN 2005af in the observed epochs is consistent with an overall asphericity of ~20% and an inclination of ~30 deg. Evidence for a more complex, evolving asphericity, possibly involving clumps in the SN 2005af envelope, is found.Comment: 6 pages, 5 figures, to be published A&

Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals

In this communication, the convergence of the 1/t and Wang - Landau algorithms in the calculation of multidimensional numerical integrals is analyzed. Both simulation methods are applied to a wide variety of integrals without restrictions in one, two and higher dimensions. The errors between the exact and the calculated values of the integral are obtained and the efficiency and accuracy of the methods are determined by their dynamical behavior. The comparison between both methods and the simple sampling Monte Carlo method is also reported. It is observed that the time dependence of the errors calculated with 1/t algorithm goes as N^{-1/2} (with N the MC trials) in quantitative agreement with the simple sampling Monte Carlo method. It is also showed that the error for the Wang - Landau algorithm saturates in time evidencing the non-convergence of the methods. The sources for the error are also determined.Comment: 8 pages, 5 figure