Search results for "MathematicsofComputing_NUMERICALANALYSIS"
showing 9 items of 149 documents
Data-Driven Interactive Multiobjective Optimization Using a Cluster-Based Surrogate in a Discrete Decision Space
2019
In this paper, a clustering based surrogate is proposed to be used in offline data-driven multiobjective optimization to reduce the size of the optimization problem in the decision space. The surrogate is combined with an interactive multiobjective optimization approach and it is applied to forest management planning with promising results. peerReviewed
Approximate Taylor methods for ODEs
2017
Abstract A new method for the numerical solution of ODEs is presented. This approach is based on an approximate formulation of the Taylor methods that has a much easier implementation than the original Taylor methods, since only the functions in the ODEs, and not their derivatives, are needed, just as in classical Runge–Kutta schemes. Compared to Runge–Kutta methods, the number of function evaluations to achieve a given order is higher, however with the present procedure it is much easier to produce arbitrary high-order schemes, which may be important in some applications. In many cases the new approach leads to an asymptotically lower computational cost when compared to the Taylor expansio…
Linear Feature Extraction for Ranking
2018
We address the feature extraction problem for document ranking in information retrieval. We then propose LifeRank, a Linear feature extraction algorithm for Ranking. In LifeRank, we regard each document collection for ranking as a matrix, referred to as the original matrix. We try to optimize a transformation matrix, so that a new matrix (dataset) can be generated as the product of the original matrix and a transformation matrix. The transformation matrix projects high-dimensional document vectors into lower dimensions. Theoretically, there could be very large transformation matrices, each leading to a new generated matrix. In LifeRank, we produce a transformation matrix so that the generat…
Fast Computation by Subdivision of Multidimensional Splines and Their Applications
2016
We present theory and algorithms for fast explicit computations of uni- and multi-dimensional periodic splines of arbitrary order at triadic rational points and of splines of even order at diadic rational points. The algorithms use the forward and the inverse Fast Fourier transform (FFT). The implementation is as fast as FFT computation. The algorithms are based on binary and ternary subdivision of splines. Interpolating and smoothing splines are used for a sample rate convertor such as resolution upsampling of discrete-time signals and digital images and restoration of decimated images that were contaminated by noise. The performance of the rate conversion based spline is compared with the…
Local cubic splines on non-uniform grids and real-time computation of wavelet transform
2017
In this paper, local cubic quasi-interpolating splines on non-uniform grids are described. The splines are designed by fast computational algorithms that utilize the relation between splines and cubic interpolation polynomials. These splines provide an efficient tool for real-time signal processing. As an input, the splines use either clean or noised arbitrarily-spaced samples. Formulas for the spline’s extrapolation beyond the sampling interval are established. Sharp estimations of the approximation errors are presented. The capability to adapt the grid to the structure of an object and to have minimal requirements to the operating memory are of great advantages for offline processing of s…
Multi-marginal entropy-transport with repulsive cost
2020
In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove the $\Gamma$-convergence of the entropy-transport functional to a multi-marginal optimal transport problem with a repulsive cost. We also prove the entropy-regularized version of the Kantorovich duality.
Reverse Catmull-Clark Subdivision
2006
Reverse subdivision consists in constructing a coarse mesh of a model from a finer mesh of this same model. In this paper, we give formulas for reverse Catmull-Clark subdivision. These formulas allow the constructing of a coarse mesh for almost all meshes. The condition for being able to apply these formulas is that the mesh to be reversed must be generated by the subdivision of a coarse mesh. Except for this condition, the mesh can be arbitrary. Vertices can be regular or extraordinary and the mesh itself can be arbitrary (triangular, quadrilateral…).
Synchronization of hidden chaotic attractors on the example of radiophysical oscillators
2017
In the present paper we consider the problem of synchronization of hidden and self-excited attractors in the context of application to a system of secure communication. The system of two coupled Chua models was studied. Complete synchronization was observed as for self-excited, as hidden attractors. Beside it for hidden attractors some special type of dynamic was revealed.
Sparse nonnegative tensor decomposition using proximal algorithm and inexact block coordinate descent scheme
2021
Nonnegative tensor decomposition is a versatile tool for multiway data analysis, by which the extracted components are nonnegative and usually sparse. Nevertheless, the sparsity is only a side effect and cannot be explicitly controlled without additional regularization. In this paper, we investigated the nonnegative CANDECOMP/PARAFAC (NCP) decomposition with the sparse regularization item using l1-norm (sparse NCP). When high sparsity is imposed, the factor matrices will contain more zero components and will not be of full column rank. Thus, the sparse NCP is prone to rank deficiency, and the algorithms of sparse NCP may not converge. In this paper, we proposed a novel model of sparse NCP w…