Numerical Algorithms最新文献

This study presents a new branch and bound algorithm designed for the global optimization of the fractional squared least squares model for GPS localization. The algorithm incorporates a novel underestimation approach that provides theoretically superior lower bounds while requiring a comparable computational effort to the current approach. Numerical results demonstrate the substantial efficiency enhancements of the proposed algorithm over the existing algorithm.

We study multivariate polynomial interpolation based on Radon projections corresponding to the intersection of hyperplanes and the coordinate axes of (mathbb {R}^n). We give a characterization of these hyperplanes which determine an interpolation polynomial uniquely. We also establish conditions such that the interpolation projectors based on Radon projections converge to the Taylor projector.

We consider the problem of maximizing the ratio of two generalized quadratic matrix form functions over the Stiefel manifold, i.e., (max limits _{X^{T}X=I} frac{text {tr}(GX^{T}AX)}{text {tr}(GX^{T}BX)}) (RQMP). We utilize the Dinkelbach algorithm to globally solve RQMP, where each subproblem is evaluated by the closed-form solution. For a special case of RQMP with (AB=BA), we propose an equivalent linear programming problem. Numerical experiments demonstrate that it is more efficient than the recent SDP-based algorithm.

In this paper, the algorithms and applications of the dual quaternion QR decomposition are studied. The direct algorithm and dual structure-preserving algorithm of dual quaternion QR decomposition utilizing Householder transformation of dual quaternion vector are proposed. Numerical experiments show that two algorithms are feasible, and the dual structure-preserving algorithm is superior to the direct algorithm in terms of computational efficiency. Therefore, the dual structure-preserving algorithm of dual quaternion QR decomposition is used to color image watermarking. Experiments illustrate that our method is feasible and better than the compared methods in anti-aggression.

This paper concentrates on the quaternion indefinite least squares (QILS) problem. Firstly, we define the quaternion J-unitary matrix and the quaternion hyperbolic Givens rotation, and study their properties. Then, based on these, we investigate the quaternion hyperbolic QR factorization, and purpose its real structure-preserving (SP) algorithm by the real representation (Q-RR) matrix of the quaternion matrix. Immediately after, we explore the solution of the QILS problem, and give a real SP algorithm of solving the QILS problem. Eventually, to illustrate the effectiveness of proposed algorithms, we offer numerical examples.

The well-known INdividual Differences SCALing (INDSCAL) model is intended for the simultaneous metric multidimensional scaling (MDS) of several doubly centered matrices of squared dissimilarities. An alternative approach, called for short DINDSCAL (direct INDSCAL), is proposed for analyzing directly the input matrices of squared dissimilarities. In the present work, the problem of fitting the DINDSCAL model to the data is formulated as a Riemannian optimization problem on a product matrix manifold comprised of the Stiefel sub-manifold of zero-sum matrices and non-negative diagonal matrices. A practical algorithm, based on the generic Riemannian trust-region method by Absil et al., is presented to address the underlying problem, which is characterized by global convergence and local superlinear convergence rate. Numerical experiments are conducted to illustrate the efficiency of the proposed method. Furthermore, comparisons with the existing projected gradient approach and some classical methods in the MATLAB toolbox Manopt are also provided to demonstrate the merits of the proposed approach.

The noncentral beta distribution function is a generalization of the central beta distribution (the regularized incomplete beta function) that includes a noncentrality parameter. This paper describes an algorithm and provides a Matlab implementation for calculating the noncentral beta distribution function. Through a series of numerical tests, we demonstrate that the algorithm is accurate and efficient across a wide range of parameters.

This paper explores numerical methods for recovering a density term in a fractional Sturm-Liouville problem using a set of spectra. By applying Lidskii’s theorem, a sequence of trace formulae are derived to elucidate the connections between the unknown coefficients and the complex eigenvalues of a fractional spectra problem. Two efficient algorithms are proposed based on these trace formulae, and their effectiveness is demonstrated through numerical experiments.

The main purpose of this paper is to develop and analyze a partially truncated Euler-Maruyama method for numerically solving SDEs with super-linear piecewise continuous drift coefficients and (varvec{(1/2+alpha )})-Hölder diffusion coefficients (PTEMH), for (varvec{alpha in [0,1/2]}). We first present an analytical form for the unique solution of such problems. Then we establish the strong convergence theory of the PTEMH scheme. We show that the convergence rate of the proposed method in the case (varvec{alpha in (0,1/2]}) reaches (varvec{alpha }), which is optimal compared to the explicit Euler-Maruyama method. Finally, numerical results are given to confirm the theoretical convergence rate.

This paper studies a type of multiterm fractional stochastic delay integro-differential equations (FSDIDEs). First, the Euler-Maruyama (EM) method is developed for solving the equations, and the strong convergence order of this method is obtained, which is (varvec{min left{ alpha _{l}-frac{1}{2}, alpha _{l}-alpha _{l-1}right} }). Then, a fast EM method is also presented based on the exponential-sum-approximation with trapezoid rule to cut down the computational cost of the EM method. In the end, some concrete numerical experiments are used to substantiate these theoretical results and show the effectiveness of the fast method.