Related papers: Fractional Newton-Raphson Method Accelerated with …
Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…
A new continuous regularized Gauss-Newton-type method with simultaneous updates of the operator $(F^{\pr*}(x(t))F'(x(t))+\ep(t) I)^{-1}$ for solving nonlinear ill-posed equations in a Hilbert space is proposed. A convergence theorem is…
We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the…
In practical applications of iterative first-order optimization, the learning rate schedule remains notoriously difficult to understand and expensive to tune. We demonstrate the presence of these subtleties even in the innocuous case when…
We reveal the fractal nature of patterns arising in random sequential adsorption of particles with continuum power-law size distribution, $P(R)\sim R^{\alpha-1}$, $R \le R_{\rm max}$. We find that the patterns become more and more ordered…
Ridge regression (RR) is a regularization technique that penalizes the L2-norm of the coefficients in linear regression. One of the challenges of using RR is the need to set a hyperparameter ($\alpha$) that controls the amount of…
We obtain integral representations of the $n$-th derivatives of the Bessel functions with respect to the order. The numerical evaluation of these expressions is very efficient using a double exponential integration strategy. Also, from the…
Two fractional two-phase Stefan-like problems are considered by using Riemann-Liouville and Caputo derivatives of order $\alpha \in (0, 1)$ verifying that they coincide with the same classical Stefan problem at the limit case when…
In this work, a second-order approximation of the fractional substantial derivative is presented by considering a modified shifted substantial Gr\"{u}nwald formula and its asymptotic expansion. Moreover, the proposed approximation is…
In this work, our aim is to introduce a symmetric fractional-order reduction (SFOR) method to develop numerical algorithms on nonuniform temporal meshes for fractional wave equations under lower regularity assumptions. The $L$-type…
The Frank-Wolfe algorithm is a popular method for minimizing a smooth convex function $f$ over a compact convex set $\mathcal{C}$. While many convergence results have been derived in terms of function values, hardly nothing is known about…
The fractional calculus framework will be used to invert the potential energy function from the classical scattering angle, which will be related to Riemann-Liouville fractional integral. Numerical solution of this fractional order problem…
In this paper, we present a convergence rate analysis for the inexact Krasnosel'skii-Mann iteration built from nonexpansive operators. Our results include two main parts: we first establish global pointwise and ergodic iteration-complexity…
In the present paper we derive the asymptotic expansion formula for the trapezoidal approximation of the fractional integral. We use the expansion formula to obtain approximations for the fractional integral of order…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
The dynamic iteration method with a restricted additive Schwarz splitting is investigated to co-simulate linear differential algebraic equations system coming from RLC electrical circuit with linear components. We show the pure linear…
We introduce an efficient algorithm for computing fractional integrals and derivatives and apply it for solving problems of the calculus of variations of fractional order. The proposed approximations are particularly useful for solving…
By using generalized fractional derivative, the parametric generalized fractional Nikiforov-Uvarov (NU) method is introduced. The second-order parametric generalized differential equation is exactly solved in the fractional form. The…
In this paper, a high-order and fast numerical method is investigated for the time-fractional Black-Scholes equation. In order to deal with the typical weak initial singularities of the solution, we construct a finite difference scheme with…
This paper studies the convergence difficulty of cohesive zone models in static analysis. It is shown that an inappropriate starting point of iterations in the Newton-Raphson method is responsible for the convergence difficulty. A simple,…