Automatic step size and order control in implicit one-step extrapolation methods

The impedance tensor corresponding to the magnetotelluric field for a nonisotropic one‐dimensional structure is given in terms of the solutions of a sixth‐order differential system. The conductivity tensor is three‐dimensional. Its components depend upon depth only in an arbitrary manner such that the corresponding matrix is positive definite. The impedance tensor components are found by a numerical integration procedure based on a set of one‐step methods and a variable step‐size to insure a given accuracy in the final result. Calculations were made for three models having sharp boundaries and also transitional layers. The first of these models has a middle layer of high conductivity, sandwiched between two layers of linearly varying conductivity, while in the second model the middle layer has a very low conductivity. In the third model the conductivity tensor is three‐dimensional and is linearly varying in one of the layers.

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Accelerated Runge-Kutta Methods

Discrete Dynamics in Nature and Society ◽

10.1155/2008/790619 ◽

2008 ◽

Vol 2008 ◽

pp. 1-38 ◽

Cited By ~ 8

Author(s):

Firdaus E. Udwadia ◽

Artin Farahani

Keyword(s):

Computationally Efficient ◽

Step Size ◽

Time Step ◽

Integration Schemes ◽

Local Accuracy ◽

Numerical Integrators ◽

One Step ◽

Runge Kutta ◽

Finite Step ◽

Proof Of Convergence

Standard Runge-Kutta methods are explicit, one-step, and generally constant step-size numerical integrators for the solution of initial value problems. Such integration schemes of orders 3, 4, and 5 require 3, 4, and 6 function evaluations per time step of integration, respectively. In this paper, we propose a set of simple, explicit, and constant step-size Accerelated-Runge-Kutta methods that are two-step in nature. For orders 3, 4, and 5, they require only 2, 3, and 5 function evaluations per time step, respectively. Therefore, they are more computationally efficient at achieving the same order of local accuracy. We present here the derivation and optimization of these accelerated integration methods. We include the proof of convergence and stability under certain conditions as well as stability regions for finite step sizes. Several numerical examples are provided to illustrate the accuracy, stability, and efficiency of the proposed methods in comparison with standard Runge-Kutta methods.

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A New Hybrid Algorithm of Trust Region Methods

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.680.442 ◽

2014 ◽

Vol 680 ◽

pp. 442-446

Author(s):

De Qing Zhang ◽

Pei Pei Zhou ◽

Qing Hua Zhou

Keyword(s):

Numerical Experiments ◽

Trust Region ◽

Acute Angle ◽

Step Size ◽

Interaction Point ◽

Trust Region Algorithms ◽

Value Range ◽

One Step ◽

Current Interaction ◽

Negative Gradient

In the solution of trust region subproblem within the classical trust region algorithms, the centre of sphere is the current interaction point and one step-size is the upper bound. Considering that only with the negative gradient direction to acute angle may reduce the function value, we introduce the parameter to control of the centre of sphere and the radius. Based on the numerical experiments, obtains the value range of the parameter. The numerical evaluation demonstrates the validity of the new trust region algorithms.

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Asymptotic Properties of One-Step Estimator Obtained from an Optimal Step Size

Econometric Theory ◽

10.1017/s0266466600010379 ◽

1987 ◽

Vol 3 (2) ◽

pp. 305-306 ◽

Cited By ~ 2

Author(s):

Whitney K. Newey

Keyword(s):

Asymptotic Properties ◽

Step Size ◽

Optimal Step Size ◽

One Step

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Overhead Line Mechanics Taking the Influence of Wind into Account

Acta Polytechnica ◽

10.14311/1642 ◽

2012 ◽

Vol 52 (5) ◽

Author(s):

Miroslav Müller

Keyword(s):

Harmonic Component ◽

Overhead Line ◽

Step Size ◽

Continuous Description ◽

Spatial Coordinates ◽

One Step ◽

Catenary Curve ◽

Harmonic Components ◽

Dynamic Description ◽

The Time Domain

This paper deals with problems of overhead line motion. The line model is based on a dynamic description of a catenary curve. The benefits of dynamic modeling in this field are decrypted, and there is an explanation of one of the models that is used. The dynamic model is derived from a string equation. The main contribution of the model is in 3D simulation of complex mechanics. The model of an overhead line shaking is generally based on the superposition of harmonic components, in particular the spatial coordinates. Each individual harmonic component is solved separately in one step of calculation, and is then combined with the other solutions. The result is a continuous description of the position of the wire along its length in both the space domain and the time domain. The model thus allows calculationsof uneven effects of forces along the length of an overhead line. The accuracy of the calculation is determined by the number of harmonics and other parameters that are calculated (e.g. step size, simulation time) The model is actually a combination of discrete and continuous calculations. Each model function block is described in the form of an equation. In the case study, ACSR 350/59 wire is analyzed. In this part of our work, an auxiliary model of wind influence was integrated into the global model.

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Optical properties of CdS/MMA dispersions and CdS/PMMA nanocomposites prepared by one-step, size-controlled synthesis

Russian Physics Journal ◽

10.1007/s11182-011-9499-1 ◽

2011 ◽

Vol 53 (8) ◽

pp. 849-856 ◽

Cited By ~ 4

Author(s):

A. A. Biryukov ◽

T. I. Izaak ◽

E. Yu. Gotovtseva ◽

I. N. Lapin ◽

A. I. Potekaev ◽

...

Keyword(s):

Optical Properties ◽

Controlled Synthesis ◽

Step Size ◽

One Step ◽

Size Controlled

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In Situ Investigation of Non-Isothermal Decomposition of Pt Acetylacetonate as One-Step Size-Controlled Synthesis of Pt Nanoparticles

physica status solidi (a) ◽

10.1002/pssa.201800488 ◽

2018 ◽

Vol 215 (23) ◽

pp. 1800488

Author(s):

Anton A. Kulbakov ◽

Mathieu Allix ◽

Aydar Rakhmatullin ◽

Alexey S. Mikheykin ◽

Yuri V. Popov ◽

...

Keyword(s):

Pt Nanoparticles ◽

Controlled Synthesis ◽

Isothermal Decomposition ◽

Step Size ◽

In Situ Investigation ◽

One Step ◽

Size Controlled

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Validation of a novel functional test for assessing metamorphopsia using epiretinal membranes as a model

Scientific Reports ◽

10.1038/s41598-020-71627-1 ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Henrietta Wang ◽

Sieu K. Khuu ◽

Sheila Lam ◽

Clarissa Lin ◽

Michael Kalloniatis ◽

...

Keyword(s):

Functional Test ◽

Proof Of Concept ◽

Step Size ◽

Macular Disease ◽

Epiretinal Membranes ◽

One Step ◽

Amsler Grid ◽

Spatial Redundancy ◽

Asymptomatic Disease ◽

Psychophysical Test

Abstract Current tests for assessing metamorphopsia do not account for confounders such as perceptual filling-in and spatial redundancy, which affect its sensitivity and repeatability. This proof-of-concept study aimed to assess the performance of a novel laboratory-based psychophysical test (Line Sag Test, LST) which addresses these issues for quantification of metamorphopsia in idiopathic epiretinal membranes. The LST quantifies perpendicular metamorphopsia at three eccentricities (3°, 6°, and 9°) along eight meridians (45° steps). Metamorphopsia was assessed using the LST and Amsler grid and the hit rates of both tests for detecting metamorphopsia were compared. Normal metamorphopsia scores using the LST did not differ significantly from 0 and fell within one step-size (p = 0.500). The LST detected significantly more cases of metamorphopsia than the Amsler grid (14/21 versus 3/21) (p = 0.003). Similarly, significantly more cases of visual distortions in asymptomatic iERMs were detected using the LST than the Amsler grid (11/18 versus 0/18) (p = 0.008). The LST has a higher hit rate compared to the Amsler grid (67% versus 14%). This work demonstrates a psychophysically-robust functional test addressing perceptual confounders is more sensitive for quantifying and localising metamorphopsia in macular disease, particularly in asymptomatic disease.

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A Pipeline for Adaptive Filtering and Transformation of Noisy Left-Arm ECG to Its Surrogate Chest Signal

Electronics ◽

10.3390/electronics9050866 ◽

2020 ◽

Vol 9 (5) ◽

pp. 866

Author(s):

Farzad Mohaddes ◽

Rafael da Silva ◽

Fatma Akbulut ◽

Yilu Zhou ◽

Akhilesh Tanneeru ◽

...

Keyword(s):

Adaptive Filtering ◽

Mean Squared Error ◽

Signal To Noise Ratio ◽

Recursive Least Squares ◽

Step Size ◽

Ecg Signals ◽

Squared Error ◽

One Step ◽

Power Line Interference ◽

Electrocardiogram Ecg

The performance of a low-power single-lead armband in generating electrocardiogram (ECG) signals from the chest and left arm was validated against a BIOPAC MP160 benchtop system in real-time. The filtering performance of three adaptive filtering algorithms, namely least mean squares (LMS), recursive least squares (RLS), and extended kernel RLS (EKRLS) in removing white (W), power line interference (PLI), electrode movement (EM), muscle artifact (MA), and baseline wandering (BLW) noises from the chest and left-arm ECG was evaluated with respect to the mean squared error (MSE). Filter parameters of the used algorithms were adjusted to ensure optimal filtering performance. LMS was found to be the most effective adaptive filtering algorithm in removing all noises with minimum MSE. However, for removing PLI with a maximal signal-to-noise ratio (SNR), RLS showed lower MSE values than LMS when the step size was set to 1 × 10−5. We proposed a transformation framework to convert the denoised left-arm and chest ECG signals to their low-MSE and high-SNR surrogate chest signals. With wide applications in wearable technologies, the proposed pipeline was found to be capable of establishing a baseline for comparing left-arm signals with original chest signals, getting one step closer to making use of the left-arm ECG in clinical cardiac evaluations.

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