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Numerical Methods for Solving Optimal Control Problem Using Scaling Boubaker Function

Eman Hassan Ouda Alfrdji, Imad Noah Ahmed
2020 Al-Qadisiyah Journal Of Pure Science  
In this paper, the approximation method was used for solving optimal control problem (OCP), two techniques for state parameterization and control parameterization have been considered with the aid of Scaling  ...  Polynomials (SBP) represent a new important technique for solving (OCP's).  ...  terms of Boubaker polynomials are Scaling Boubaker polynomials (SBP) The Scaling Boubaker polynomials (SBP), can be defined as follows: ( ) = 2 (2 − 2 − 1) ≤ ≤ 0 ℎ … (7) The arguments of scaling (k  ... 
doi:10.29350/qjps.2020.25.2.1120 fatcat:zxogvveagbe3vekpuntb7efx2e

An application of fast factorization algorithms in Computer Aided Geometric Design

G. Casciola, F. Fabbri, L.B. Montefusco
2003 Linear Algebra and its Applications  
For the numerical solution to this problem we propose an algebraic approach, based on a fast factorization algorithm of the resulting Bezout matrix with polynomial entries, which avoids the need for symbolic  ...  Numerical examples and comparisons with other standard intersection methods are given.  ...  (a) the evaluation of the determinant of a matrix with polynomial entries; (b) the evaluation of the K real roots, in [0, 1], of the resulting (m · n)-degree polynomial;(c) the realization of Gaussian  ... 
doi:10.1016/s0024-3795(02)00469-x fatcat:z6j5cfk2pje3dablzpegi73u5a

Evaluating the Jones polynomial with tensor networks [article]

Konstantinos Meichanetzidis, Stefanos Kourtis
2018 arXiv   pre-print
By sampling random knots via a grid-walk procedure and computing the full tensor trace, we demonstrate numerically that the Jones polynomial can be evaluated in time that scales subexponentially with the  ...  This allows us to evaluate the Jones polynomial of knots that are too complex to be treated with other available methods.  ...  The favorable typical-case scaling allows us to comfortably evaluate the Jones polynomial at q = 5 for knots with n c > 40.  ... 
arXiv:1807.02119v1 fatcat:jaolbo7a4zhndjkaa3ypqm4b2e

Exact evaluation of limits and tangents for non-polynomial subdivision schemes

S. Schaefer, J. Warren
2008 Computer Aided Geometric Design  
The values for this exact evaluation scheme can be computed via a simple system of linear equation derived from the scaling relations associated with the scheme or, equivalently, as the dominant left eigenvector  ...  of an upsampled subdivision matrix associated with the scheme.  ...  For schemes with explicit piecewise polynomial definitions, computing the exact position of points on associated curves or surfaces corresponds to just evaluating the appropriate polynomial at a particular  ... 
doi:10.1016/j.cagd.2008.06.005 fatcat:6hz2wmmy6vbwrj7vlijzruw2lm

Calibration of analog scales based on a metrological comparison between the SIM Guide and OIML R 76-1

Jose Daniel Hernandez-Vasquez, Cristian Pedraza-Yepes, Oscar Fabian Higuera-Cobos, Javier Pedroza Caballero, Wilmer de Los Reyes Montes
2018 Contemporary Engineerng Sciences  
(ii) reformulate the cost / benefit criteria for the calibration of scales, once it is known that better results can be obtained by the application of a particular method; (iii) analyze an unquestionable  ...  different tests carried out, the results consolidated in this research will give solid tools to a metrology laboratory: (i) define a classification of the methods that offer the lowest uncertainty associated with  ...  Thus, this paper was addressed with the main focus of evaluating these tests. So, three analog scales of the baby weighing type.  ... 
doi:10.12988/ces.2018.88447 fatcat:udbtxz3n6bhp3gswpktalxzcmu

FFT-based Computation of Polynomial Coefficients and Related Tasks [article]

Hans-Rudolf Thomann
2016 arXiv   pre-print
evaluate the symmetric functions of a set of parameters.  ...  We present a FFT-based algorithm for the computation of a polynomial's coefficients from its roots, and apply it to obtain the coefficients of interpolation polynomials, to invert Vandermondians and to  ...  While previously the NaN condition arose during evaluation of 2 with > 1 due to overflow, now it occurs additionally when all vanish after re-scaling with < 1 due to underflow, Circle Roots and data  ... 
arXiv:1608.01357v1 fatcat:g4tiwbeol5gvhm4chhchaokley

Exact Evaluation of Non-Polynomial Subdivision Schemes at Rational Parameter Values

Scott Schaefer, Joe Warren
2007 15th Pacific Conference on Computer Graphics and Applications (PG'07)  
The values for this exact evaluation scheme can be computed via a simple system of linear equation derived from the scaling relations associated with the scheme or, equivalently, as the dominant left eigenvector  ...  of an upsampled subdivision matrix associated with the scheme.  ...  For schemes with explicit piecewise polynomial definitions, computing the exact position of points on associated curves or surfaces corresponds to just evaluating the appropriate polynomial at a particular  ... 
doi:10.1109/pg.2007.8 dblp:conf/pg/SchaeferW07 fatcat:ugqyv3veofevdmiwcsyutljvsa

Fourier-based and Rational Graph Filters for Spectral Processing [article]

Giuseppe Patanè
2021 arXiv   pre-print
Approximating arbitrary graph filters with rational polynomials provides a more accurate and numerically stable alternative with respect to polynomials.  ...  , shape correspondence), and filters (e.g., polynomial, rational polynomial), and (ii) a spectrum-free computation with a generally low computational cost and storage overhead.  ...  Evaluating the spectral kernel/wavelet at one scale with the rational approximation is generally more efficient and accurate than the truncated spectral approximation, especially at small scales (Fig.  ... 
arXiv:2011.04055v2 fatcat:6jg725dmwnej5b7fr5pzz3iz2a

Predicting Final User Satisfaction Using Momentary UX Data and Machine Learning Techniques

Kitti Koonsanit, Nobuyuki Nishiuchi
2021 Journal of Theoretical and Applied Electronic Commerce Research  
This study shows that participants' momentary UX can be understood using a support vector machine (SVM) with a polynomial kernel and that momentary UX can be used to make more accurate predictions about  ...  However, there is no comprehensive UX evaluation method for time-continuous situations during the use of products or services.  ...  Scale Data) Dataset II: 5 Classes (5-Point Scale Data) Polynomial Kernel Polynomial Kernel Score Polynomial Kernel SVM SVM with Oversampling into the Polynomial Kernel SVM SVM with Oversampling into the  ... 
doi:10.3390/jtaer16070171 fatcat:owlgmpkqqrfm3a2rvr5xm5by3y

Gradient Boosts the Approximate Vanishing Ideal

Hiroshi Kera, Yoshihiko Hasegawa
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Specifically, we exploit the gradient to (i) sidestep the spurious vanishing problem in polynomial time to remove symbolically trivial redundant bases, (ii) achieve consistent output with respect to the  ...  translation and scaling of input, and (iii) remove nontrivially redundant bases.  ...  Without this property, linear scaling on the input leads to nonlinear scaling on the evaluation of the output polynomials; thus, a consistent result cannot be obtained regardless of how well is chosen.  ... 
doi:10.1609/aaai.v34i04.5869 fatcat:ssmvsxtivnbpxcg6ca3djgbu3q

Automatic Target Classification in GMTI Airborne Scenario

Mousumi Gupta, Debasish Bhaskar, Rabindranath Bera
2016 International Journal of Technology  
The RCS feature is evaluated using the Chebyshev polynomial.  ...  Finally, the classifier with the Chebyshev polynomial feature has been tested with an unknown RCS value.  ...  The scaled-data feature has been evaluated by using the Chebyshev polynomial technique.  ... 
doi:10.14716/ijtech.v7i5.2925 fatcat:l6kapf7aare5nfqdmklimxxxru

Some Computational Aspects of Discrete Orthonormal Moments

R. Mukundan
2004 IEEE Transactions on Image Processing  
The recursive procedure used for polynomial evaluation can be suitably modified to reduce the accumulation of numerical errors.  ...  The proposed set of moments can be used for representing image shape features and for reconstructing an image from its moments with a high degree of accuracy.  ...  This can be done by modifying the scale factor in (3) as (9) If we denote the new set of polynomials with the above scale factor, by , then it can be easily seen that the recurrence relations given in  ... 
doi:10.1109/tip.2004.828430 pmid:15326847 fatcat:hdvoemswgfg6thutahja6jblca

Fast methods for resumming matrix polynomials and Chebyshev matrix polynomials

WanZhen Liang, Roi Baer, Chandra Saravanan, Yihan Shao, Alexis T Bell, Martin Head-Gordon
2004 Journal of Computational Physics  
A few numerical tests are presented, showing that evaluation of matrix functions via polynomial expansions can be preferable when the matrix is sparse and these fast resummation algorithms are employed  ...  Fast and effective algorithms are discussed for resumming matrix polynomials and Chebyshev matrix polynomials.  ...  First, it should be possible to obtain speedups relative to function evaluation via diagonalization because diagonalization scales cubically with matrix dimension while polynomial evaluation can scale  ... 
doi:10.1016/j.jcp.2003.08.027 fatcat:kpf3rdijpzdqjlybes3ifujfsi

Fast evaluation and locality of overlap fermions

W. Bietenholz, I. Hip, K. Schilling
2002 Nuclear Physics B - Proceedings Supplements  
We show that its polynomial evaluation is accelerated considerably compared to the standard Neuberger fermion. In addition the degree of locality is strongly improved.  ...  Again, the Wilson spectrum is very broad to start with, and re-scaling usually leads to small δ, whereas it is kept larger for the HF.  ...  POLYNOMIAL OVERLAP EVALUA-TION AND LOCALITY We consider two ways to evaluate the overlap Dirac operator by means of polynomial expansions, which have appeared in the literature. 1) We introduce the Hermitean  ... 
doi:10.1016/s0920-5632(01)01857-6 fatcat:eiua6kifsvdhlhleteyt6tn3mm

An Iterative Method for Solving Quadratic Optimal Control Problem Using Scaling Boubaker Polynomials

Imad Noah Ahmed, Eman Hassan Ouda
2020 Open Science Journal  
In this paper, an iteration method was used for solving a quadratic optimal control problem (QOCP) by the aid of state parameterization technique and scaling Boubaker polynomials.  ...  The process steps were illustrated by some numerical examples with graphs done by Matlab.  ...  -Repeating the first iteration with more terms of the scaling Boubaker polynomial for the second and third iterations, evaluating the Ji's and compare their values with respect to J exact.  ... 
doi:10.23954/osj.v5i2.2538 fatcat:jqij3lm45bdw5byfm4mxs34som
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