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Asymptotic Convergence Rate (asymptotic + convergence_rate)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Convergence rates toward the travelling waves for a model system of the radiating gas

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2007
Masataka Nishikawa
Abstract The present paper is concerned with an asymptotics of a solution to the model system of radiating gas. The previous researches have shown that the solution converges to a travelling wave with a rate (1 + t),1/4 as time t tends to infinity provided that an initial data is given by a small perturbation from the travelling wave in the suitable Sobolev space and the perturbation is integrable. In this paper, we make more elaborate analysis under suitable assumptions on initial data in order to obtain shaper convergence rates than previous researches. The first result is that if the initial data decays at the spatial asymptotic point with a certain algebraic rate, then this rate reflects the time asymptotic convergence rate. Precisely, this convergence rate is completely same as the spatial convergence rate of the initial perturbation. The second result is that if the initial data is given by the Riemann data, an admissible weak solution, which has a discontinuity, converges to the travelling wave exponentially fast. Both of two results are proved by obtaining decay estimates in time through energy methods with suitably chosen weight functions. Copyright © 2006 John Wiley & Sons, Ltd. [source]

A new investigation of the extended Krylov subspace method for matrix function evaluations

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2010
L. Knizhnerman
Abstract For large square matrices A and functions f, the numerical approximation of the action of f(A) to a vector v has received considerable attention in the last two decades. In this paper we investigate theextended Krylov subspace method, a technique that was recently proposed to approximate f(A)v for A symmetric. We provide a new theoretical analysis of the method, which improves the original result for A symmetric, and gives a new estimate for A nonsymmetric. Numerical experiments confirm that the new error estimates correctly capture the linear asymptotic convergence rate of the approximation. By using recent algorithmic improvements, we also show that the method is computationally competitive with respect to other enhancement techniques. Copyright © 2009 John Wiley & Sons, Ltd. [source]

On the use of non-local prior densities in Bayesian hypothesis tests

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2010
Valen E. Johnson
Summary., We examine philosophical problems and sampling deficiencies that are associated with current Bayesian hypothesis testing methodology, paying particular attention to objective Bayes methodology. Because the prior densities that are used to define alternative hypotheses in many Bayesian tests assign non-negligible probability to regions of the parameter space that are consistent with null hypotheses, resulting tests provide exponential accumulation of evidence in favour of true alternative hypotheses, but only sublinear accumulation of evidence in favour of true null hypotheses. Thus, it is often impossible for such tests to provide strong evidence in favour of a true null hypothesis, even when moderately large sample sizes have been obtained. We review asymptotic convergence rates of Bayes factors in testing precise null hypotheses and propose two new classes of prior densities that ameliorate the imbalance in convergence rates that is inherited by most Bayesian tests. Using members of these classes, we obtain analytic expressions for Bayes factors in linear models and derive approximations to Bayes factors in large sample settings. [source]

Necessary and sufficient local convergence condition of one class of iterative aggregation,disaggregation methods

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2008
Ivana Pultarová
Abstract This paper concludes one part of the local convergence analysis of a certain class of iterative aggregation,disaggregation methods for computing a stationary probability distribution vector of an irreducible stochastic matrix B. We show that the local convergence of the algorithm is determined only by the sparsity pattern of the matrix and by the choice of the aggregation groups. We introduce the asymptotic convergence rates of the normalized components of approximations corresponding to particular aggregation groups and we also specify an upper bound on the rates. Copyright © 2008 John Wiley & Sons, Ltd. [source]