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Adaptive Fourier decomposition (AFD) has been found to be among the most effective greedy algorithms. AFD shows an outstanding performance in signal analysis and system identification. As compensation of effectiveness, the computation complexity is great, that is especially due to maximal selections of the parameters. In this paper, we explore the discretization of the 1-D AFD integration via with discrete Fourier transform (DFT), incorporating fast Fourier transform (FFT). We show that the new algorithm, called FFT-AFD, reduces the computational complexity from O ( M N 2 ) to O ( M N log N ) , the latter being the same as FFT. Through experiments, we verify the effectiveness, accuracy, and robustness of the proposed algorithm. The proposed FFT-based algorithm for AFD lays a foundation for its practical applications. [ABSTRACT FROM AUTHOR]

In this paper, we consider a feasible primal–dual interior point method for linear semidefinite programming problem ( S D P ) based on Alizadeh–Haeberly–Overton ( AHO ) direction (Monteiro, 1997). Firstly, and by a new and simple technique, we establish the existence and uniqueness of optimal solution of the perturbed problem ( S D P ) μ and its convergence to optimal solution of ( S D P ) . Next, we present new different alternatives to calculate the displacement step. After, we establish the convergence of the obtained algorithm and we show that its complexity is O ( n ln [ ε − 1 ( 〈 X 0 , S 0 〉 ) ] ) . Finally, we present some numerical simulations which show the effectiveness of the algorithm developed in this work. [ABSTRACT FROM AUTHOR]

Existing principal curve algorithms have some drawbacks such as time consuming and narrow application scope in practice, since these algorithms are mainly based on global optimization. In this paper, we present the concept of Constraint Local Principal Curve (CLPC), which uses local optimization methods and restricts the principal curve with two fixed endpoints to reduce the computational complexity. In addition, we propose three CLPC algorithms by Local Optimization and Adaptive Radius to expand the range of applications and increase the solution quality. The first algorithm, i.e., CLPCg is based on greedy thinking. The second algorithm, i.e., CLPCs uses one dimensional search and the last algorithm CLPCc combines the greedy thinking and one dimensional search. Then, we define six performance indices to evaluate the performance of the CLPC algorithms. Finally, we present some numerical experiments with three simulation data sets and two GPS measured data sets in both highway and railway. The results indicate that all of the three CLPC algorithms can obtain high-accuracy data from multiple low-accuracy data efficiently. The CLPC algorithms can improve the accuracy and computational speed compared with the existing K-segment principal curve (KPC) algorithm. In addition, CLPCc outperforms CLPCg and CLPCs according to the comprehensive experiments while CLPCg runs much faster than other ones. [ABSTRACT FROM AUTHOR]

Abstract: A modification of the Ikebe algorithm for computing the lower half of the inverse of an (unreduced) upper Hessenberg matrix, extended to compute the entries of the superdiagonal, is considered in this paper. It enables us to compute the inverse of a quasiseparable Hessenberg matrix in times. A new factorization expressing the inverse of a nonsingular Hessenberg matrix as a product of two suitable matrices is obtained. Because this allows us the use of back substitution for the inversion of triangular matrices, the inverse is computed with complexity . Some comparisons with results obtained using other recent inversion algorithms are also provided. [Copyright &y& Elsevier]

Abstract: In this paper we propose a new finite element frequency domain (FEFD) method to compute the band spectra of 2D photonic crystals without impurities. Exploiting periodicity to identify discretization points differing by a period, it increases the effectiveness of the algorithm and reduces significantly its computational complexity. The results of an extensive experimentation indicate that our method offers an effective alternative to the most quoted methods in the literature. [Copyright &y& Elsevier]

Abstract: This paper presents a new directional multilevel algorithm for solving -body or -point problems with highly oscillatory kernels. We address the problem by first proving that the interaction between a ball of radius and a well-separated region has an approximate low rank representation, as long as the well-separated region belongs to a cone with a spanning angle of and is at a distance which is at least away from the ball. Based on this representation, our algorithm organizes the high frequency computation using a multidirectional and multiscale strategy. Our algorithm is proved to have an optimal computational complexity for any given accuracy when the points are sampled from a two-dimensional surface. [Copyright &y& Elsevier]

Abstract: In this paper, we present a new algorithm to solve general linear fifth-order boundary value problems (BVPs) in the reproducing kernel space . Representation of the exact solution is given in the reproducing kernel space. Its approximate solution is obtained by truncating the -term of the exact solution. Some examples are displayed to demonstrate the computational efficiency of the method. [Copyright &y& Elsevier]

Abstract: In this paper, a stochastic gradient descent algorithm is proposed for the binary classification problems based on general convex loss functions. It has computational superiority over the existing algorithms when the sample size is large. Under some reasonable assumptions on the hypothesis space and the underlying distribution, the learning rate of the algorithm has been established, which is faster than that of closely related algorithms. [Copyright &y& Elsevier]

Abstract: Exclusion algorithms have been used recently to find all solutions of a system of nonlinear equations or to find the global minimum of a function over a compact domain. These algorithms are based on a minimization condition that can be applied to each cell in the domain. In this paper, we consider Lipschitz functions of order and give a new minimization condition for the exclusion algorithm. Furthermore, convergence and complexity results are presented for such algorithm. [Copyright &y& Elsevier]

Abstract: The stereolithography (STL) file format, developed for rapid prototyping industry, became an attractive alternative for surface representation in solid modeling. In this paper, an algorithm for the surface discretization of 3D models in STL format is presented. Initially, a boundary representation is reconstructed from the STL file format using feature recognition. Then a smooth surface is recovered over the original STL grid by adopting the interpolating subdivision procedure. And finally, the recovered surface is subjected to the triangulation accomplished using the advancing front technique operating directly on the surface. [Copyright &y& Elsevier]

In this paper, efficient simultaneous strategies are presented for the optimization of practical problems involving PDE-models. In particular, reduced sequential quadratic programming methods for problems with only few influence variables and simultaneous quadratic programming iterations are discussed. As a result we obtain algorithms whose overall computational complexity is reduced considerably in comparison to a black-box approach. [Copyright &y& Elsevier]

Digital nets are among the most successful methods to construct low-discrepancy point sets for quasi-Monte Carlo integration. Their quality is traditionally assessed by a measure called the t -value. A refinement computes the t -value of the projections over subsets of coordinates and takes a weighted average (or some other function) of these values. It is also of interest to compute the t -values of embedded nets obtained by taking subsets of the points. In this paper, we propose an efficient algorithm to compute such measures and we compare our approach with previously proposed methods both empirically and in terms of computational complexity. [ABSTRACT FROM AUTHOR]