scholarly journals A study on optimally constructed compactly supported orthogonal wavelet filters

2021 ◽  
pp. 52-52
Author(s):  
Yongkai Fan ◽  
Qian Hu ◽  
Yun Pan ◽  
Chaosheng Huang ◽  
Chao Chen ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Orthogonal Wavelet ◽  
Initial Value ◽  
Vanishing Moments ◽  
Type Method ◽  
Wavelet Filters ◽  
Compactly Supported ◽  
Elementary Method ◽  
Newton Iteration Method

Compactly supported orthogonal wavelet filters are extensively applied to the analysis and description of abrupt signals in fields such as multimedia. Based on the application of an elementary method for compactly supported orthogonal wavelet filters and the construction of a system of nonlinear equations for filter coefficients, we design compactly supported orthogonal wavelet filters, in which both the scaling and wavelet functions have many vanishing moments, by approximately solving the system of nonlinear equations. However, when solving such a system about filter coefficients of compactly supported wavelets, the most widely used method, the Newton Iteration method, cannot converge to the solution if the selected initial value is not near the exact solution. For such, we propose optimization algorithms for the Gauss-Newton type method that expand the selection range of initial values. The proposed method is optimal and promising when compared to other works, by analyzing the experimental results obtained in terms of accuracy, iteration times, solution speed, and complexity.

A new fourth order Newton-type method for solution of system of nonlinear equations

2015 ◽  
Vol 270 ◽  
pp. 724-730 ◽  
Author(s):  
Waseem Asghar Khan ◽  
Khalida Inayat Noor ◽  
Kaleemulah Bhatti ◽  
Faryal Aijaz Ansari
Keyword(s):  
Nonlinear Equations ◽  
Fourth Order ◽  
System Of Nonlinear Equations ◽  
Type Method

Solving System of Nonlinear Equations using Genetic Algorithm

2019 ◽  
Vol 10 (4) ◽  
pp. 877-886 ◽  
Author(s):  
Chhavi Mangla ◽  
Musheer Ahmad ◽  
Moin Uddin
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations

An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

2012 ◽  
Vol 220-223 ◽  
pp. 2585-2588
Author(s):  
Zhong Yong Hu ◽  
Fang Liang ◽  
Lian Zhong Li ◽  
Rui Chen
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Sixth Order ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

Study on the working state of the five hundred-meter aperture spherical telescope using step-wise assignment method

2014 ◽  
Vol 229 (2) ◽  
pp. 316-324 ◽  
Author(s):  
Yu Liu ◽  
Feng Gao
Keyword(s):  
Nonlinear Equations ◽  
Analytical Solutions ◽  
Driving Mechanism ◽  
Initial Value ◽  
Unknown Parameters ◽  
Support Structure ◽  
Assignment Method ◽  
New Type ◽  
Set Up ◽  
The Mathematical Model

The working state of the five hundred-meter aperture spherical telescope (FAST) is solved using the step-wise assignment method. In this paper, the mathematical model of the cable-net support structure of the FAST is set up by the catenary equation. There are a large number of nonlinear equations and unknown parameters of the model. The nonlinear equations are solved by using the step-wise assignment method. The method is using the analytical solutions of the cable-net equations of one working state as the initial value for the next working state, from which the analytical solutions of the nonlinear equations of the cable-net for each working state of the FAST and the tension and length of each driving cable can be obtained. The suggested algorithm is quite practically well suited to study the working state of the cable-net structures of the FAST. Also, the working state analysis result of the cable-net support structure of a reduced model of the cable-net structure reflector for the FAST is given to verify the reliability of the method. In order to show the validity of the method, comparisons with another algorithm to set the initial value are presented. This method has an important guiding significance to the further study on the control of the new type of flexible cable driving mechanism, especially the FAST.

scholarly journals An optimal and low computational cost fractional Newton-type method for solving nonlinear equations

2021 ◽  
pp. 107650
Author(s):  
Giro Candelario ◽  
Alicia Cordero ◽  
Juan R. Torregrosa ◽  
María P. Vassileva
Keyword(s):  
Nonlinear Equations ◽  
Computational Cost ◽  
Type Method ◽  
Low Computational Cost

A unified framework for the design of low-complexity wavelet filters

2017 ◽  
Vol 15 (06) ◽  
pp. 1750054 ◽  
Author(s):  
Ameya K. Naik ◽  
Raghunath S. Holambe
Keyword(s):  
Feature Extraction ◽  
Compact Support ◽  
Low Complexity ◽  
Design Parameters ◽  
Unified Framework ◽  
Vanishing Moments ◽  
Wavelet Filters ◽  
Design Variables ◽  
Optimum Filter ◽  
Simulation Results

An outline is presented for construction of wavelet filters with compact support. Our approach does not require any extensive simulations for obtaining the values of design variables like other methods. A unified framework is proposed for designing halfband polynomials with varying vanishing moments. Optimum filter pairs can then be generated by factorization of the halfband polynomial. Although these optimum wavelets have characteristics close to that of CDF 9/7 (Cohen-Daubechies-Feauveau), a compact support may not be guaranteed. Subsequently, we show that by proper choice of design parameters finite wordlength wavelet construction can be achieved. These hardware friendly wavelets are analyzed for their possible applications in image compression and feature extraction. Simulation results show that the designed wavelets give better performances as compared to standard wavelets. Moreover, the designed wavelets can be implemented with significantly reduced hardware as compared to the existing wavelets.

Sign in / Sign up

Export Citation Format

Share Document