‎in this paper‎, ‎a spectral tau method for solving fractional riccati‎ ‎differential equations is considered‎. ‎this technique describes‎ ‎converting of a given fractional riccati differential equation to a‎ ‎system of nonlinear algebraic equations by using some simple‎ ‎matrices‎. ‎we use fractional derivatives in the caputo form‎. ‎convergence analysis of the proposed method is given an...

The wavelet transform-domain least-mean square (WTDLMS) algorithm uses the self-orthogonalizing technique to improve the convergence performance of LMS. In WTDLMS algorithm, the trade-off between the steady-state error and the convergence rate is obtained by the fixed step-size. In this paper, the WTDLMS adaptive algorithm with variable step-size (VSS) is established. The step-size in each subf...

in this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$i$-statistical convergence and‎ ‎$i$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{n}$) and‎ ‎introduce the notions of $i$-statis...

Improved convergence rate estimates are derived for a variant of Aronszajn-type intermediate problems that is both computationally feasible and convergent for problems with nontrivial essential spectra. In a previous paper the authors obtained rate of convergence estimates for this method in terms of containment gaps between subspaces. In the present work, techniques for estimating relatively u...

3 Local convergence rate: simple case 2 3.1 Theorem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.2 Main estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.3 Convergence rate of the sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.4 Proof of the theorem . . . . . . . . . . . . . . ....

We prove the trace-norm convergence of the Trotter product formula for nonself-adjoint Gibbs semigroups. For any m-sectorial generators A and B such that e ?tRe A is in the trace-class for t > 0, the Trotter product formula converges in the trace-norm. With smallness conditions on B with respect to A, we give error bound estimates of the convergence rate in this topology.

Let fn(X) be the nth iterate of a function in some interval [0, c]. It is known that if f(x) xxc, a > 1, then fn(X) An for some A and a. In this paper we prove a converse of this theorem: The rate of convergence of the iterates determines the form of a function.

The probabilistic properties of eigenvalues of random matrices whose dimension increases indefinitely has received considerable attention. One important aspect is the existence and identification of the limiting spectral distribution (LSD) of the empirical distribution of the eigenvalues. When the LSD exists, it is useful to know the rate at which the convergence holds. The main method to estab...

We extend the approach of Walker (2003, 2004) to the case of misspecified models. A sufficient condition for establishing rates of convergence is given based on a key identity involving martingales, which does not require construction of tests. We also show roughly that the result obtained by using tests can also be obtained by our approach, which demonstrates the potential wider applicability ...

In a simple, forward looking linear stochastic model we investigate the impact of heterogeneity in expectations formation on the speed of convergence of the learning process of agents towards equilibrium. We …nd that even when heterogeneity does not a¤ect learnability in term of its asymptotic outcome, it can still have an important impact on the learnability of an equilibrium in terms of the s...