1
Department of Mathematics, Tafresh University, Tafresh, Iran
2
Department of Electrical Engineering, Tafresh University, Tafresh, Iran
10.22052/scj.2024.253276.1169
Abstract
The least square error method yields acceptable results in system identification. The process of parameter estimation helps solve the linear equation . The important point is that the normal method of solving the above problem has a computational complexity for an matrix. In solving this problem, the computational complexity increases with the increase of (the size of the data matrix). On the other hand, availability of more samples leads to better modeling of the system. In the practical problems of system identification, when the number of input data is large the computational complexity increases greatly. Recently, in the field of quantum computing, some algorithms have been presented that significantly reduce the computational complexity. Among the most important of them is the HHL algorithm, which solves the above linear equation in time, where is the condition number and s is the sparsity of the matrix. In this article, the goal is to present the developed quantum algorithm for solving the problem of least square error identification (GLS method). In this article, two classical-quantum and all-quantum methods are presented. Unlike conventional HHL methods, the proposed methods in this article are able to calculate unbiased parameters with non-Hermitian matrices, and color noise. The proposed classical-quantum method has a computational complexity of of and the all-quantum method has an order of in relation to the size of the data matrix. The results and comparisons show that the methods proposed in the article have less complexity and limitations than classical methods such as psudeo-inverse complexity).
Ramezani, M., Kalantari, S., & Madadi, A. (2024). Parameter Estimation of a Linear Regression Model By Extending Least Square Method Based on Quantum Computing. Soft Computing Journal, (), -. doi: 10.22052/scj.2024.253276.1169
MLA
Mehdi Ramezani; Sadegh Kalantari; Ali Madadi. "Parameter Estimation of a Linear Regression Model By Extending Least Square Method Based on Quantum Computing". Soft Computing Journal, , , 2024, -. doi: 10.22052/scj.2024.253276.1169
HARVARD
Ramezani, M., Kalantari, S., Madadi, A. (2024). 'Parameter Estimation of a Linear Regression Model By Extending Least Square Method Based on Quantum Computing', Soft Computing Journal, (), pp. -. doi: 10.22052/scj.2024.253276.1169
VANCOUVER
Ramezani, M., Kalantari, S., Madadi, A. Parameter Estimation of a Linear Regression Model By Extending Least Square Method Based on Quantum Computing. Soft Computing Journal, 2024; (): -. doi: 10.22052/scj.2024.253276.1169
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