In 1980, Rabin proposed a probabilistic algorithm to solve a higher-order equation over a finite field. When his algorithm is applied to the quadratic equation on a finite field, the probability that the desired
We will use the theory developed in the preceding section as the basis for describing a variety of methods that can be used for image interpolation. We shall assume that the image is to be enlarged by integer factors C× D, where for convenience, we assume that both C and D are even....
It includes algorithms such as Shor's algorithm, Grover's algorithm, Deutsch-Jozsa algorithm, Simon's algorithm, and Bernstein-Vazirani algorithm, which provide exponential or quadratic speedup for solving specific problems. These algorithms have applications in various areas of computer science. AI ...
While the solution to deriving the roots of the general quadratic equation is adequately covered in a typical classroom environment, the same is not true for the general cubic and quartic equations. To the best of our knowledge, we do not see the roots of the general cubic or quartic equatio...
This study introduces an enhanced self-adaptive wild goose algorithm (SAWGA) for solving economical-environmental-technical optimal power flow (OPF) problems in traditional and modern energy systems. Leveraging adaptive search strategies and robust diversity capabilities, SAWGA distinguishes itself from clas...
In this work, we implement XL on graphics processing unit (GPU) and evaluate its solving time for the MQ problem over several small finite fields, namely, $\\mathrm{GF}(2)$, $\\mathrm{GF}(3)$, $\\mathrm{GF}(5)$, and $\\mathrm{GF}(7)$. Our implementations can solve MQ ...
This paper shows that the inverse chirp z-transform (ICZT), which generalizes the inverse fast Fourier transform (IFFT) off the unit circle in the complex plane, can also be used with chirp contours that perform partial or multiple revolutions on the uni
Although there are many methods proposed for evaluation of image definition, most of them are sensitive to noise and variations of lens magnification and light condition and may result in the local peaks of the image definition values during the auto-focusing process. To address these problems, we...
In this paper, we introduce a new iterative algorithm for solving a generalized Sylvester matrix equation of the form $\sum_{t=1}^{p}A_{t}XB_{t}=C$ which includes a class of linear matrix equations. The objective of the algorithm is to minimize an error
for Hammerstein state time-delay models. Let E denote an expectation operator and ||X||2≔tr[XXT] be the norm of the matrix X. Since v(t) is a white noise, forming a quadratic cost function, J1(θ)=E[‖y(t)−φT(t)θ‖2], and minimizing J1(θ) lead to the following sto...