Original Research Article

Article volume = 2022 and issue = 2

Pages: 181–190

Article publication Date: November 21, 2022

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# Discrete Sampling Analysis for Electricity Market Forecasting with Reproducing Kernel Hilbert Space

#### Mohammadreza Foroutan(a) and Farzad Farzanfar(b)

(a) Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.

(b) Department of Computer Engineering and Information Technology, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran.

##### Abstract:

Analyse discrete sampling theories in the reproducing kernel Hilbert space are applied here to whole-sale electricity market forecasting problem. We consider the optimal approximation of any function be longing to the kernel across pricing nodes and hours via a sampling method. Then, a necessary and sufficient condition to perfectly reconstruct the function in the corresponding reproducing kernel Hilbert space of function is investigated. The key idea of our work is adopting the reproducing kernel Hilbert space corresponding to the Gramian matrix of the additive tensor kernel and considering the orthogonal projector by the kernel functions. We also give numerical examples, using the sampling theorem, to confirm the behavior of the proposed method.

##### Keywords:

Gramian matrix, Hilbert space, Orthogonal projector, Reproducing kernel, discrete Sampling theorem.

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##### Cite this article as:

- Mohammadreza Foroutan and Farzad Farzanfar, Discrete Sampling Analysis for Electricity Market Forecasting with Reproducing Kernel Hilbert Space, Communications in Combinatorics, Cryptography & Computer Science, 2022(2), PP.181–190, 2022
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