Application of Accelerated Iterative Method in Calculating Wave Length in Harbor Engineering

2011 ◽  
Vol 130-134 ◽  
pp. 3481-3484
Author(s):  
Shou Jun Wang ◽  
Ming Wei Wei
Keyword(s):  
Iterative Method ◽  
Calculation Method ◽  
Iteration Method ◽  
Wave Length ◽  
Newton Iteration ◽  
Convergence Speed ◽  
Iteration Formula ◽  
Convergence Results ◽  
Computing Speed

In this paper, a specific application accelerated iterative method is presented for calculating wave length in harbor engineering, which includes calculation method of wave length and specific implement in Excel. Different wavelengths into the iteration formula to calculate the same result can be obtained, but the calculation speed of different methods have significant differences to arrive at the fastest method . Calculated by accelerating the iteration method can significantly increase the computing speed and calculation steps. After the derivation of several methods and calculations show that Newton iteration is the fastest way to convergence speed, in the practical range of about 10 steps through the iterative convergence results can be obtained.

scholarly journals Heron’s cubic root iteration method with a new approach

2021 ◽  
Author(s):  
S. Gadtia ◽  
S. K. Padhan
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Interpolation Formula ◽  
Alternative Proof ◽  
New Approach ◽  
Iteration Formula ◽  
Odd Order ◽  
Even Order ◽  
Lagrange’S Method

Abstract Heron’s cubic root iteration formula conjectured by Wertheim is proved and extended for any odd order roots. Some possible proofs are suggested for the roots of even order. An alternative proof of Heron’s general cubic root iterative method is explained. Further, Lagrange’s interpolation formula for nth root of a number is studied and found that Al-Samawal’s and Lagrange’s method are equivalent. Again, counterexamples are discussed to justify the effectiveness of the present investigations.

Blind Image Separation Based on an Optimized Fast Fixed Point Algorithm

2013 ◽  
Vol 756-759 ◽  
pp. 3578-3583 ◽  
Author(s):  
Wei Yuan ◽  
Li Yi Zhang
Keyword(s):  
Fixed Point ◽  
Iteration Method ◽  
Newton Iteration ◽  
Convergence Speed ◽  
Experimental Results ◽  
Fixed Point Algorithm ◽  
Adaptive Enhancement ◽  
Image Separation ◽  
Newton Iteration Method ◽  
Blind Image

An optimized fast fixed point algorithm based on modified Newton iteration method has been proposed. With good performance ofthe blind image separation, the optimized algorithm can improve the convergence speed greatly.We proposed a new adaptive enhancement parameter to enhance the separated images effectively. The experimental results demonstrate that the new algorithm is superior.

A new modified group explicit iterative method for the numerical solution of time dependent viscous Burgers' equation

2014 ◽  
Vol 05 (02) ◽  
pp. 1350029 ◽  
Author(s):  
Jyoti Talwar ◽  
R. K. Mohanty
Keyword(s):  
Iterative Method ◽  
Numerical Solution ◽  
Convergence Analysis ◽  
Iterative Methods ◽  
Iteration Method ◽  
Burgers Equation ◽  
Time Dependent ◽  
Alternating Group ◽  
Explicit Method ◽  
Rectangular Coordinates

In this article, we discuss a new smart alternating group explicit method based on off-step discretization for the solution of time dependent viscous Burgers' equation in rectangular coordinates. The convergence analysis for the new iteration method is discussed in details. We compared the results of Burgers' equation obtained by using the proposed iterative method with the results obtained by other iterative methods to demonstrate computationally the efficiency of the proposed method.

scholarly journals The Picard-HSS-SOR iteration method for absolute value equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Lin Zheng
Keyword(s):  
Iteration Method ◽  
Numerical Experiments ◽  
Absolute Value Equation ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
Convergence Results ◽  
Hss Iteration ◽  
The Absolute ◽  
Hss Iteration Method

AbstractIn this paper, we present the Picard-HSS-SOR iteration method for finding the solution of the absolute value equation (AVE), which is more efficient than the Picard-HSS iteration method for AVE. The convergence results of the Picard-HSS-SOR iteration method are proved under certain assumptions imposed on the involved parameter. Numerical experiments demonstrate that the Picard-HSS-SOR iteration method for solving absolute value equations is feasible and effective.

scholarly journals A Preconditioned Iteration Method for Solving Sylvester Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jituan Zhou ◽  
Ruirui Wang ◽  
Qiang Niu
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Newton's Iteration ◽  
Gradient Based ◽  
Selection Of

A preconditioned gradient-based iterative method is derived by judicious selection of two auxil- iary matrices. The strategy is based on the Newton’s iteration method and can be regarded as a generalization of the splitting iterative method for system of linear equations. We analyze the convergence of the method and illustrate that the approach is able to considerably accelerate the convergence of the gradient-based iterative method.

Extension of Iteration Method for Determining Strain Distributions to the Uniformly Stressed Plate With a Hole

1963 ◽  
Vol 30 (2) ◽  
pp. 210-214 ◽  
Author(s):  
E. A. Davis
Keyword(s):  
Iterative Method ◽  
Strain Hardening ◽  
Iteration Method ◽  
Incompressible Materials

The iterative method for determining strain distributions is applied to a uniformly stressed plate with a hole at the center. The method is not limited to incompressible materials; the load can be raised in incremental amounts; and strain-hardening of the material can be taken into consideration.

scholarly journals Statistical Process Monitoring with Biogeography-Based Optimization Independent Component Analysis

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Xiangshun Li ◽  
Di Wei ◽  
Cheng Lei ◽  
Zhiang Li ◽  
Wenlin Wang
Keyword(s):  
Fault Detection ◽  
Independent Component Analysis ◽  
Process Monitoring ◽  
Iteration Method ◽  
Newton Iteration ◽  
Independent Component ◽  
Statistical Process ◽  
Independent Components ◽  
Newton Iteration Method ◽  
Statistical Process Monitoring

Independent Component Analysis (ICA), a type of typical data-driven fault detection techniques, has been widely applied for monitoring industrial processes. FastICA is a classical algorithm of ICA, which extracts independent components by using the Newton iteration method. However, the choice of the initial iterative point of Newton iteration method is difficult; sometimes, selection of different initial iterative points tends to show completely different effects for fault detection. So far, there is still no good strategy to get an ideal initial iterative point for ICA. To solve this problem, a modified ICA algorithm based on biogeography-based optimization (BBO) called BBO-ICA is proposed for the purpose of multivariate statistical process monitoring. The Newton iteration method is replaced with BBO here for extracting independent components. BBO is a novel and effective optimization method to search extremes or maximums. Comparing with the traditional intelligent optimization algorithm of particle swarm optimization (PSO) and so on, BBO behaves with stronger capability and accuracy of searching for solution space. Moreover, numerical simulations are finished with the platform of DAMADICS. Results demonstrate the practicability and effectiveness of BBO-ICA. The proposed BBO-ICA shows better performance of process monitoring than FastICA and PSO-ICA for DAMADICS.

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