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Motivation and Overview
Published in Naim A. Kheir, Systems Modeling and Computer Simulation, 2018
Rather than imitating a physical phenomenon, as on an analog computer, a digital computer operates in a logical manner in solving the mathematical model of a system numerically. On a digital computer the variables are discretely defined (in contrast with the continuous nature in analog simulation); variables are defined only at specified intervals of time (the independent variable). Digital signals are binary in nature and are represented by a two-state signal, with the higher voltage level called the “one” state and the lower voltage called the “zero” state level. The basic digital computer can be divided into logic elements and storage elements, thus allowing the performance of a variety of arithmetic and logical functions, as well as storage of information. The physical subsystems of a general-purpose digital computer are the input, control, storage (memory), arithmetic, and output units. Possible basic arithmetic operations are counting, addition, subtraction, multiplication, and division. Floating-point arithmetic and digital computer large memory are among its important features. Also, the need for magnitude scaling is eliminated owing to floating-point arithmetic operations and the capability of representing a wide range of variables. However, the need to use analog/digital (A/D) and digital/analog (D/A) converters results in “quantization errors” that may be significant.
Matrices
Published in Bilal M. Ayyub, Richard H. Mccuen, Numerical Analysis for Engineers, 2015
Bilal M. Ayyub, Richard H. Mccuen
The primary arithmetic operations are addition, subtraction, multiplication, and division. Matrix algebra has operations called matrix addition, subtraction, and multiplication; there is no operation called matrix division. Instead, a matrix operation called matrix inversion is available. Each of these matrix operations is discussed in this section.
Novel Adaptive Sine Cosine Arithmetic Optimization Algorithm For Optimal Automation Control of DG Units and STATCOM Devices
Published in Smart Science, 2023
The AOA firstly proposed by Laith Abualigah et. al [27], is a new metaheuristic method inspired from the basic arithmetic operators well known in mathematics such as Multiplication (Mul ‘×’), Division (Div ‘÷’), Subtraction (Sub‘-‘), and Addition (Add ‘+’). The AOA is a population based algorithm, and like many metaheuristic optimization methods, the algorithm, starts by creating randomly an initial population considered as an initial solution, then the population is evaluated using one or two objective functions, and the application of two coordinated mechanism search known as intensification and diversification to find the near optimal solution. The performances of the proposed AOA have been validated by authors in [27] on many benchmark functions and various real engineering problems [27]. Obtained results compared to several recent global optimization methods show the superiority and competitive of the AOA.
An enhanced arithmetic optimization algorithm for global maximum power point tracking of photovoltaic systems under dynamic irradiance patterns
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2022
AOA is a recently recognized algorithm, and simple mathematical arithmetic operations inspire intelligence. The arithmetic operators are division “D,” multiplication “M,” subtraction “S,” and addition “A.” The D & M explore the solutions, and S & A exploit the solutions in a search area. The ranking of the operators in a search space as D > M > S > A. The search will start at D and end at A. It is successfully applied to an MPPT problem to find the GMPP (Mirza et al. 2021; Zhang, Yang, and Chen 2022). The “N” number of duty cycles (di, i = 1, 2, 3, N) are considered solutions, and the objective function is to maximize the generated PV power given in (3) and (4).
Neighborhood optimization of intelligent wireless mobile network based on big data technology
Published in International Journal of Computers and Applications, 2021
The time complexity of the algorithm is usually measured by the number of arithmetic operations such as addition, subtraction, multiplication and division required to complete the algorithm. This paper evaluates their time complexity by comparing the time required for different algorithms to complete the same prediction. Secondly, the prediction accuracy is analyzed, because time series prediction is not a percentage. If the predicted value of time series is lower than the set error range, the predicted result is correct. In addition, the predicted accuracy can also be judged according to the arithmetic average or standard average value of the predicted error. Finally, the predicted stability is analyzed, and the predicted stability can be divided into three categories. The stability of the results in one prediction, the second is the stability of the results of different prediction times under the same initial condition, and the third is the stability of the long-term and short-term prediction results.