Finding ε-Global Optimal Value of a One-dimensional Periodic Function in an Interval Based on Fourier Series and Semi-definite Programming

2011 ◽  
Author(s):  
Hua Chen ◽  
Churen Sun
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
One Dimensional ◽  
Optimal Value ◽  
Global Optimal

Numerical Inversion of Laplace Transform for Time Resolved Thermal Characterization Experiment

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
J. Toutain ◽  
J.-L. Battaglia ◽  
C. Pradere ◽  
J. Pailhes ◽  
A. Kusiak ◽  
...  
Keyword(s):  
Fourier Series ◽  
Laplace Transform ◽  
Periodic Function ◽  
Thermal Characterization ◽  
Inverse Laplace Transform ◽  
Numerical Inversion ◽  
Time Resolved ◽  
Reliable Technique ◽  
Numerical Inverse Laplace Transform ◽  
Thermal Disturbance

The aim of this technical brief is to test numerical inverse Laplace transform methods with application in the framework of the thermal characterization experiment. The objective is to find the most reliable technique in the case of a time resolved experiment based on a thermal disturbance in the form of a periodic function or a distribution. The reliability of methods based on the Fourier series methods is demonstrated.

scholarly journals Fourier Series with Small Gaps

2006 ◽  
Vol 13 (3) ◽  
pp. 581-584
Author(s):  
Rajendra G. Vyas
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Fourier Coefficients ◽  
Lacunary Series ◽  
Lacunary Fourier Series

Abstract Let 𝑓 be a 2π-periodic function in 𝐿1[–π, π] and be its lacunary Fourier series with small gaps. We have estimated Fourier coefficients of 𝑓 if it is of φ∧ 𝐵𝑉 locally. We have also obtained a precise interconnection between the lacunarity in such series and the localness of the hypothesis to be satisfied by the generic function which allows us to the interpolate the results concerning lacunary series and non-lacunary series.

Nonlinear Inverse Heat Conduction With a Moving Boundary: Heat Flux and Surface Recession Estimation

1999 ◽  
Vol 121 (3) ◽  
pp. 708-711 ◽  
Author(s):  
V. Petrushevsky ◽  
S. Cohen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fourier Series ◽  
Heat Conduction ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Variable Order ◽  
Inverse Heat Conduction ◽  
One Dimensional

A one-dimensional, nonlinear inverse heat conduction problem with surface ablation is considered. In-depth temperature measurements are used to restore the heat flux and the surface recession history. The presented method elaborates a whole domain, parameter estimation approach with the heat flux approximated by Fourier series. Two versions of the method are proposed: with a constant order and with a variable order of the Fourier series. The surface recession is found by a direct heat transfer solution under the estimated heat flux.

24.—Mean-square Convergence of Non-harmonic Trigonometrical Series

1976 ◽  
Vol 75 (4) ◽  
pp. 297-323
Author(s):  
J. Cossar
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Mean Square ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Real Numbers ◽  
Trigonometrical Series ◽  
Fixed Positive Number ◽  
Mean Square Convergence ◽  
The Difference

SynopsisThe series considered are of the form , where Σ | cn |2 is convergent and the real numbers λn (the exponents) are distinct. It is known that if the exponents are integers, the series is the Fourier series of a periodic function of locally integrable square (the Riesz-Fischer theorem); and more generally that if the exponents are not necessarily integers but are such that the difference between any pair exceeds a fixed positive number, the series is the Fourier series of a function of the Stepanov class, S2, of almost periodic functions.We consider in this paper cases where the exponents are subject to less stringent conditions (depending on the coefficients cn). Some of the theorems included here are known but had been proved by other methods. A fuller account of the contents of the paper is given in Sections 1-5.

scholarly journals On approximation in generalized Zygmund class

2019 ◽  
Vol 52 (1) ◽  
pp. 370-387
Author(s):  
Hare Krishna Nigam
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Conjugate Function ◽  
Degree Of Approximation ◽  
Zygmund Class ◽  
Conjugate Fourier Series ◽  
Product Method ◽  
Hausdorff Means

AbstractHere, we estimate the degree of approximation of a conjugate function {\tilde g} and a derived conjugate function {\tilde g'} , of a 2π-periodic function g \in Z_r^\lambda , r ≥ 1, using Hausdorff means of CFS (conjugate Fourier series) and CDFS (conjugate derived Fourier series) respectively. Our main theorems generalize four previously known results. Some important corollaries are also deduced from our main theorems. We also partially review the earlier work of the authors in respect of order of the Euler-Hausdorff product method.

scholarly journals Time-Splitting Procedures for the Numerical Solution of the 2D Advection-Diffusion Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
A. R. Appadu ◽  
H. H. Gidey
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Optimization Technique ◽  
Step Size ◽  
One Dimensional ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Optimal Value ◽  
Time Splitting ◽  
Dispersion And Dissipation Errors

We perform a spectral analysis of the dispersive and dissipative properties of two time-splitting procedures, namely, locally one-dimensional (LOD) Lax-Wendroff and LOD (1, 5) [9] for the numerical solution of the 2D advection-diffusion equation. We solve a 2D numerical experiment described by an advection-diffusion partial differential equation with specified initial and boundary conditions for which the exact solution is known. Some errors are computed, namely, the error rate with respect to theL1norm, dispersion and dissipation errors. Lastly, an optimization technique is implemented to find the optimal value of temporal step size that minimizes the dispersion error for both schemes when the spatial step is chosen as 0.025, and this is validated by numerical experiments.

scholarly journals A bridging method for global optimization

1999 ◽  
Vol 41 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Y. Liu ◽  
K. L. Teo
Keyword(s):  
Global Optimization ◽  
Differentiable Function ◽  
Numerical Solutions ◽  
Finite Interval ◽  
Optimization Problems ◽  
Optimal Solutions ◽  
Numerical Examples ◽  
One Dimensional ◽  
Differentiable Functions ◽  
Global Optimal

AbstractIn this paper a bridging method is introduced for numerical solutions of one-dimensional global optimization problems where a continuously differentiable function is to be minimized over a finite interval which can be given either explicitly or by constraints involving continuously differentiable functions. The concept of a bridged function is introduced. Some properties of the bridged function are given. On this basis, several bridging algorithm are developed for the computation of global optimal solutions. The algorithms are demonstrated by solving several numerical examples.

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