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When applying Dynamic Power Management (DPM) technique to pervasively deployed embedded systems, the technique needs to be very efficient so that it is feasible to implement the technique on low end processor and tight-budget memory.…
This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Reduced…
We present a powerful and easy-to-implement iterative algorithm for solving large-scale optimization problems that involve $L_1$/total-variation (TV) regularization. The method is based on combining the Alternating Directions Method of…
A review of the authors's results is given. Several methods are discussed for solving nonlinear equations $F(u)=f$, where $F$ is a monotone operator in a Hilbert space, and noisy data are given in place of the exact data. A discrepancy…
A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…
This paper introduces a novel approach to address inherent limitations in the Residual Power Series (RPS) method and its variants with Laplace-like transforms when applied to solving time-fractional differential equations. Existing methods,…
The classic Alternating Direction Method of Multipliers (ADMM) is a popular framework to solve linear-equality constrained problems. In this paper, we extend the ADMM naturally to nonlinear equality-constrained problems, called neADMM. The…
The Fast Multipole Method (FMM) computes pairwise interactions between particles with an efficiency that scales linearly with the number of particles. The method works by grouping particles based on their spatial distribution and…
In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves…
We propose a numerical method, based on the shift-and-invert power iteration, that answers whether a symmetric matrix is positive definite ("yes") or not ("no"). Our method uses randomization. But, it returns the correct answer with high…
Pendry and MacKinnon meaningful discretization of Maxwell's equations was put forward specifically as part of a finite-element numerical algorithm. By contrast with a numerical approach, in the same spirit evoked by the relationships…
Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…
Finding integer solutions to norm form equations is a classical Diophantine problem. Using the units of the associated coefficient ring, we can produce sequences of solutions to these equations. It is known that these solutions can be…
In this study, we focus on identifying solution and an unknown space-dependent coefficient in a space-time fractional differential equation by employing fractional Taylor series method. The substantial advantage of this method is that we…
The traffic matrix estimation (TME) problem has been widely researched for decades of years. Recent progresses in deep generative models offer new opportunities to tackle TME problems in a more advanced way. In this paper, we leverage the…
A fractional Adomian decomposition method for fractional nonlinear differential equations is proposed. The iteration procedure is based on Jumarie's fractional derivative. An example is given to elucidate the solution procedure, and the…
In this paper, we study how the D-iteration algorithm can be applied to numerically solve the differential equations such as heat equation in 2D or 3D. The method can be applied on the class of problems that can be addressed by the…
The direct computation method(DCM) is developed to calculate the multi-loop amplitude for general masses and external momenta. The ultraviolet divergence is under control in dimensional regularization. In this paper we report on the…