scholarly journals Starting an ODE solver. [Selection of initial step size]

1977 ◽  
Author(s):  
L.F. Shampine
Keyword(s):  
Initial Step ◽  
Step Size ◽  
Initial Step Size ◽  
Selection Of

scholarly journals Automatic selection of the initial step size for an ODE solver

1987 ◽  
Vol 18 (2) ◽  
pp. 175-192 ◽  
Author(s):  
I. Gladwell ◽  
L.F. Shampine ◽  
R.W. Brankin
Keyword(s):  
Initial Step ◽  
Step Size ◽  
Automatic Selection ◽  
Initial Step Size ◽  
Selection Of

An Adaptive Invasive Weed Optimization Algorithm

2015 ◽  
Vol 29 (02) ◽  
pp. 1559004 ◽  
Author(s):  
Shuo Peng ◽  
A.-J. Ouyang ◽  
Jeff Jun Zhang
Keyword(s):  
Optimization Algorithm ◽  
Initial Step ◽  
Local Extremum ◽  
Invasive Weed Optimization ◽  
Step Size ◽  
Invasive Weed ◽  
Adaptive Step Size ◽  
Initial Step Size ◽  
Adaptive Step ◽  
Optimization Search

With regards to the low search accuracy of the basic invasive weed optimization algorithm which is easy to get into local extremum, this paper proposes an adaptive invasive weed optimization (AIWO) algorithm. The algorithm sets the initial step size and the final step size as the adaptive step size to guide the global search of the algorithm, and it is applied to 20 famous benchmark functions for a test, the results of which show that the AIWO algorithm owns better global optimization search capacity, faster convergence speed and higher computation accuracy compared with other advanced algorithms.

scholarly journals Improved Generalized Sparsity Adaptive Matching Pursuit Algorithm Based on Compressive Sensing

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zhao Liquan ◽  
Ma Ke ◽  
Jia Yanfei
Keyword(s):  
Matching Pursuit ◽  
Initial Step ◽  
Convergence Speed ◽  
One Dimension ◽  
Measurement Matrix ◽  
Improved Method ◽  
Reconstruction Accuracy ◽  
Step Size ◽  
Matching Pursuit Algorithm ◽  
Initial Step Size

The modified adaptive orthogonal matching pursuit algorithm has a lower convergence speed. To overcome this problem, an improved method with faster convergence speed is proposed. In respect of atomic selection, the proposed method computes the correlation between the measurement matrix and residual and then selects the atoms most related to residual to construct the candidate atomic set. The number of selected atoms is the integral multiple of initial step size. In respect of sparsity estimation, the proposed method introduces the exponential function to sparsity estimation. It uses a larger step size to estimate sparsity at the beginning of iteration to accelerate the algorithm convergence speed and a smaller step size to improve the reconstruction accuracy. Simulations show that the proposed method has better performance in terms of convergence speed and reconstruction accuracy for one-dimension signal and two-dimension signal.

scholarly journals Improved Short Memory Principle Method for Solving Fractional Damped Vibration Equations

2020 ◽  
Vol 10 (21) ◽  
pp. 7566
Author(s):  
Ruiqun Ma ◽  
Jinglong Han ◽  
Xiaoxuan Yan
Keyword(s):  
Initial Step ◽  
Binomial Coefficient ◽  
Degree Of Freedom ◽  
Step Size ◽  
Single Degree Of Freedom ◽  
Memory Time ◽  
Short Memory ◽  
Short Memory Principle ◽  
Initial Step Size ◽  
Two Degree Of Freedom

In this paper, an improved short memory principle based on the Grünwald–Letnikov definition is proposed and applied in solving fractional vibration differential equations. The improved idea is to adjust the truncation of memory time in short memory principle (SMP) to the truncation of binomial coefficient terms, and the finite coefficients are repeatedly applied to the step size gradually enlarged. In this method, a very small initial step size is used to meet the accuracy requirements, and then the step size is gradually enlarged to prolong the memory time and reduce the amount of calculation. Examples of free vibration, forced vibration with a single-degree-of-freedom and a vehicle suspension two-degree-of-freedom vibration reduction model verify the method’s accuracy and effectiveness.

An improved first order reliability method based on modified Armijo rule and interpolation-based backtracking scheme

2020 ◽  
pp. 1748006X2095989
Author(s):  
Sheng-Tong Zhou ◽  
Di Wang ◽  
Qian Xiao ◽  
Jian-min Zhou ◽  
Hong-Guang Li ◽  
...  
Keyword(s):  
Structural Reliability ◽  
Limit State ◽  
Initial Step ◽  
State Function ◽  
Computationally Efficient ◽  
Step Size ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method ◽  
Initial Step Size

Hasofer-Lind and Rackwtiz-Fiessler (HLRF) method is an efficient iterative algorithm for locating the most probable failure point and calculating the first order reliability index in structural reliability analysis. However, this method may encounter numerical instability problems for high nonlinear limit state function (LSF). In this paper, an improved HLRF-based first order reliability method is developed based on a modified Armijo line search rule and an interpolation-based step size backtracking scheme to improve the robustness and efficiency of the original HLRF method. Compared with other improved HLRF-based methods, the proposed method can not only guarantee the global convergence but also adaptively estimate some sensitive algorithm parameters, such as initial step size, step-size reduction coefficient, using the current known iterative information. Ten selected examples with high nonlinear LSFs are used to compare the robustness and efficiency of the proposed method with the original HLRF method and the improved HLRF (iHLRF) method. Results indicate that the proposed method is not only more computationally efficient but also less sensitive to the remaining user-defined algorithm parameters than the iHLRF method.

scholarly journals Data Set for the Reporting of Malignant Odontogenic Tumors: Explanations and Recommendations of the Guidelines From the International Collaboration on Cancer Reporting

2018 ◽  
Vol 143 (5) ◽  
pp. 587-592 ◽  
Author(s):  
Pieter J. Slootweg ◽  
Edward W. Odell ◽  
Daniel Baumhoer ◽  
Roman Carlos ◽  
Keith D. Hunter ◽  
...  
Keyword(s):  
International Collaboration ◽  
Case Series ◽  
Initial Step ◽  
Odontogenic Tumors ◽  
Data Set ◽  
Expert Opinions ◽  
Organ Systems ◽  
Standardized Reporting ◽  
Selection Of ◽  
Cancer Reporting

A data set has been developed for the reporting of excisional biopsies and resection specimens for malignant odontogenic tumors by members of an expert panel working on behalf of the International Collaboration on Cancer Reporting, an international organization established to unify and standardize reporting of cancers. Odontogenic tumors are rare, which limits evidence-based support for designing a scientifically sound data set for reporting them. Thus, the selection of reportable elements within the data set and considering them as either core or noncore is principally based on evidence from malignancies affecting other organ systems, limited case series, expert opinions, and/or anecdotal reports. Nevertheless, this data set serves as the initial step toward standardized reporting on malignant odontogenic tumors that should evolve over time as more evidence becomes available and functions as a prompt for further research to provide such evidence.

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