Modified frame algorithm and its convergence acceleration by Chebyshev method

Authors

  • Mohsen Kolahdouz Department of mathematics, Faculty of mathematical sciences, Vali-e-Asr University of Rafsanjan,
Abstract:

The aim of this paper is to improve the convergence rate of frame algorithm based on Richardson iteration and Chebyshev methods. Based on Richardson iteration method, we first square the existing convergence rate of frame algorithm which in turn the number of iterations would be bisected and increased speed of convergence is achieved. Afterward, by using Chebyshev polynomials, we improve this speed too. The importance of these methods is better understood when using frame has ill conditional number (The ratio of the upper bound to the lower bound).

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Chebyshev acceleration of the GeneRank algorithm∗

The ranking of genes plays an important role in biomedical research. The GeneRank method of Morrison et al. [11] ranks genes based on the results of microarray experiments combined with gene expression information, for example from gene annotations. The algorithm is a variant of the well known PageRank iteration, and can be formulated as the solution of a large, sparse linear system. Here we sh...

full text

Accuracy, Resolution, and Stability Properties of a Modified Chebyshev Method

While the Chebyshev pseudospectral method provides a spectrally accurate method, integration of partial differential equations with spatial derivatives of order M requires time steps of approximately O(N−2M ) for stable explicit solvers. Theoretically, time steps may be increased to O(N−M ) with the use of a parameter, α-dependent mapped method introduced by Kosloff and Tal-Ezer [J. Comput. Phy...

full text

Modified Frame Reconstruction Algorithm for Compressive Sensing

Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm generalises and extends previous iterative hard thresholding algorithms and we give sufficient conditions for successful reconstruction of the original data signal. In...

full text

A modified Chebyshev pseudospectral DD algorithm for the GBH equation

In this paper, a Chebyshev spectral collocation domain decomposition (DD) semidiscretization by using a grid mapping, derived by Kosloff and Tal-Ezer in space is applied to the numerical solution of the generalized Burger’s–Huxley (GBH) equation. To reduce roundoff error in computing derivatives we use the above mentioned grid mapping. In this work, we compose the Chebyshev spectral collocation...

full text

Coupled Harmonic Equations , SOR , and Chebyshev Acceleration

A coupled pair of harmonic equations is solved by the application of Chebyshev acceleration to the Jacobi, Gauss-Seidel, and related iterative methods, where the Jacobi iteration matrix has purely imaginary (or zero) eigenvalues. Comparison is made with a block SOR method used to solve the same problem. Introduction. In [4], we proposed a general block SOR method for solving the biharmonic equa...

full text

Modified interactive chebyshev algorithm (MICA) for non-convex multiobjective programming

In this paper, we describe an interactive procedural algorithm for convex multiobjective programming based upon the Tchebycheff method, Wierzbicki’s reference point approach, and the procedure of Michalowski and Szapiro. At each iteration, the decision maker (DM) has the option of expressing his or her objective-function aspirations in the form of a reference criterion vector. Also, the DM has ...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 4  issue 3 (Special issue)

pages  81- 95

publication date 2018-07-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023