Search results for "MathematicsofComputing_NUMERICALANALYSIS"
showing 10 items of 149 documents
Scalable Dense Factorizations for Heterogeneous Computational Clusters
2008
This paper discusses the design and the implementation of the LU factorization routines included in the Heterogeneous ScaLAPACK library, which is built on top of ScaLAPACK. These routines are used in the factorization and solution of a dense system of linear equations. They are implemented using optimized PBLAS, BLACS and BLAS libraries for heterogeneous computational clusters. We present the details of the implementation as well as performance results on a heterogeneous computing cluster.
The PCHIP subdivision scheme
2016
In this paper we propose and analyze a nonlinear subdivision scheme based on the monotononicity-preserving third order Hermite-type interpolatory technique implemented in the PCHIP package in Matlab. We prove the convergence and the stability of the PCHIP nonlinear subdivision process by employing a novel technique based on the study of the generalized Jacobian of the first difference scheme. MTM2011-22741
New descent rules for solving the linear semi-infinite programming problem
1994
The algorithm described in this paper approaches the optimal solution of a continuous semi-infinite linear programming problem through a sequence of basic feasible solutions. The descent rules that we present for the improvement step are quite different when one deals with non-degenerate or degenerate extreme points. For the non-degenerate case we use a simplex-type approach, and for the other case a search direction scheme is applied. Some numerical examples illustrating the method are given.
Control of a nonlinear continuous bioreactor with bifurcation by a type-2 fuzzy logic controller
2008
The object of this paper is the application of a type-2 fuzzy logic controller to a nonlinear system that presents bifurcations. A bifurcation can cause instability in the system or can create new working conditions which, although stable, are unacceptable. The only practical solution for an efficient control is the use of high performance controllers that take into account the uncertainties of the process. A type-2 fuzzy logic controller is tested by simulation on a nonlinear bioreactor system that is characterized by a transcritical bifurcation. Simulation results show the validity of the proposed controllers in preventing the system from reaching bifurcation and instable or undesirable s…
Color Correction for Image Stitching by Monotone Cubic Spline Interpolation
2015
This paper proposes a novel color correction scheme for image stitching where the color map transfer is modelled by a monotone Hermite cubic spline and smoothly propagated into the target image. A three-segments monotone cubic spline minimizing color distribution statistics and gradient differences with respect to both the source and target images is used. While the spline model can handle non-linear color maps, the minimization over the gradient differences limits strong alterations on the image structure. Adaptive heuristics are introduced to reduce the minimization search space and thus computational time. Experimental comparisons with respect to the state-of-the-art linear mapping model…
A fixed point theorem for uniformly locally contractive mappings in a C-chainable cone rectangular metric space
2011
Recently, Azam, Arshad and Beg [ Banach contraction principle on cone rectangular metric spaces, Appl. Anal. Discrete Math. 2009] introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we introduce the notion of c-chainable cone rectangular metric space and we establish a fixed point theorem for uniformly locally contractive mappings in such spaces. An example is given to illustrate our obtained result.
Polynomial mapped bases: theory and applications
2022
Abstract In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial mapped bases allowing, for instance, to incorporate data or function discontinuities in a suitable mapping function. The new technique substantially mitigates the Runge’s and Gibbs effects.
Cubic Local Splines on Non-uniform Grid
2015
In this chapter, two types of local cubic splines on non-uniform grids are described: 1. The simplest variation-diminishing splines and 2. The quasi-interpolating splines. The splines are computed by a simple fast computational algorithms that utilizes a relation between the splines and cubic interpolation polynomials. Those splines can serve as an efficient tool for real-time signal processing. As an input, they use either clean or noised arbitrarily-spaced samples. On the other hand, the capability to adapt the grid to the structure of an object and minimal requirements to the operating memory are great advantages for off-line processing of signals and multidimensional data arrays.
Biorthogonal Wavelet Transforms Originating from Splines
2015
This chapter describes how to design families of biorthogonal wavelet transforms of signals and respective biorthogonal Wavelet bases in the signal space using spline-based prediction filters. Although the designed Wavelets originate from splines, they are not splines themselves. The design and implementation of the biorthogonal Wavelet transforms is done using the Lifting scheme. Most of the filters participating in the expansion of signals over the presented bases have infinite impulse responses and are implemented by recursive filtering whose computational cost is competitive with the FIR filtering cost. Properties of the designed Wavelets, such as symmetry, flat spectra, good time domai…
Periodic Orthogonal Wavelets and Wavelet Packets
2018
In this chapter, we discuss how to derive versatile families of periodic discrete-time orthogonal wavelets and wavelet packets from discrete and discrete-time splines outlined in Chap. 3. These wavelets and wavelet packets, although not having compact supports, are well localized in the time domain. They can have any number of discrete vanishing moments. Their DFT spectra tend to have a rectangular shape when the spline order grows and provide a collection of refined splits of the Nyquist frequency band. The wavelet and wavelet packet transforms are implemented in a fast way using the FFT.