Number Of Iterations Research Articles

Optimizing robotic arm control using deep Q-learning and artificial neural networks through demonstration-based methodologies: A case study of dynamic and static conditions

This paper uses robot programming techniques, such as Deep Q Network, Artificial Neural Network, and Artificial Deep Q Network, to address challenges related to controlling robotic arms through demonstration learning. Static and dynamic states of the subjects were the subjects of experiments. Each method's classification accuracy process success values and experimental condition combination were evaluated. The DQN method demonstrated favourable classification accuracy outcomes, achieving an Accuracy value of 0.64 for the fixed dice and 0.52 for the moving dice. The Response value was 0.51 for the fixed dice and 0.41 for the moving dice, indicating a moderate level. The ANN method demonstrated lower accuracy, with Accuracy values of 0.59 and 0.56 and Response values of 0.61 and 0.58, respectively. The ADQN method demonstrated superior outcomes, with Accuracy values of 0.66 and 0.59 and Response values of 0.67 and 0.61. During the initial learning iterations, ADQN demonstrated the highest success rate at 33.67 %, whereas DQN and ANN achieved 28.39 % and 20.13 % success rates, respectively. As the number of iterations increased, all methods demonstrated improvement in their results. ADQN maintained a high success rate of 97.59 %, while DQN and ANN attained 82.16 % and 88.66 %, respectively. As the number of iterations increases, the results of all methods improve, but the success rate of the Artificial Deep Q Network remains high. As the number of iterations increases, both Deep Q Network and Artificial Neural Network demonstrate the potential to achieve good results. Overall, the findings support the efficacy of robot programming techniques that incorporate demonstration learning. The Artificial Deep Q Network is the most successful and fast-converging method suitable for various robot control tasks. These findings provide a foundation for future research and large-scale, comprehensive learning applications for complex rot control.

IBPF-RRT*: An improved path planning algorithm with Ultra-low number of iterations and stabilized optimal path quality

Due to its asymptotic optimality, the Rapidly-exploring Random Tree star (RRT*) algorithm is widely used for robotic operations in complex environments. However, the RRT* algorithm suffers from poor path quality, slow convergence, and unstable generation of high-quality paths in the path planning process. This paper proposes an Improved Bi-Tree Obstacle Edge Search Artificial Potential Field RRT* algorithm (IBPF-RRT*) to address these issues. First, based on the RRT* algorithm, this paper proposes a new obstacle edge search artificial potential field strategy (ESAPF), which speeds up the path search and improves the path quality simultaneously. Second, a bi-directional pruning strategy is designed to optimize the bi-directional search tree branch nodes and combine the bi-directional search strategy to reduce the number of iterations for convergence speed significantly. Third, a novel path optimization strategy is proposed, which enables high-quality paths to be generated stably by creating an entirely new node between two path nodes and then optimizing the paths using a pruning strategy based on triangular inequalities. Experimental results in three different scenarios show that the proposed IBPF-RRT* algorithm outperforms other methods in terms of optimal path quality, algorithm stability, and the number of iterations when compared to the RRT*, Q-RRT*, PQ-RRT*, F-RRT* and CCPF-RRT* algorithms, and proves the effectiveness of the proposed three strategies.

An efficient volume-preserving binary filter for additive manufacturing in topology optimization

Topology optimization faces challenges concerning grey transition regions, manufacturability and computational efficiency. This article introduces an approach called the volume-preserving binary (VPB) filter. This novel sensitivity/density filter, based on a determinant-based matrix approach, efficiently detects grey elements and produces completely binary designs. The VPB filter addresses volume preservation by accurately expressing the volume-preserving condition, i.e. the volume before filtering equals the volume of solid materials after filtering. Comparison with other filtering methods, including the volume-preserving Heaviside filter and the Heaviside projection, illustrates the superior clarity and speed of the VPB filter. It reduces the number of iterations required for topology optimization, from hundreds or thousands to only tens of iterations, making it a promising solution for practical applications where manufacturability and computational efficiency are principal. Examples on compliance optimization, compliant mechanisms and heat conduction demonstrate the VPB filter's effectiveness in providing satisfactory solutions while perfectly preserving the length scale.

An intelligent obfuscated mobile malware detection using deep supervised learning algorithms

Obfuscated mobile malware (OMM) is a malicious software in mobile that hides to avoid detection and annihilation. These types of malwares are thorny to identify due to their inevitable nature. Deep learning (DL) algorithms are the most desirable to detect obfuscated malware based on the ‘n’ number of iterations with adjustable weights and neurons. This study investigates the accurate detection of OMM using significant DL algorithms such as multi-layer perceptron (MLP), self-organizing maps (SOM), long short-term memory (LSTM) networks, auto encoders (AE), and convolutional neural network (CNN) based on appropriate parameter tuning. The dataset taken for the study is CICMalMem2022 that contains 58,596 samples with 57 features which is basically designed for OMM detection. The dataset comprises Spyware, Ransomware, Trojan horse, and Benign. The DL models are evaluated based on performance metrics such as precision, recall, accuracy, training accuracy, test accuracy, validation accuracy, training loss, validation loss and receiver operating characteristic (ROC) curve. Based on the experimental evaluation, the study reveals that LSTM outperforms with 100% accuracy and MLP achieves 99.9% accuracy in detecting and classifying the OMM using deep supervised learning (SL) mechanism.

Estimation of ultrasonic flight time based on SHADE algorithm and extended kalman filtering

Abstract Traditional methods of using ultrasound to measure oxygen concentration have the issue of inaccuracy and susceptibility to noise interference when measuring the time of flight (TOF) of ultrasonic echo signals. A proposed algorithm for ultrasonic parameter estimation, utilizing an asymmetric Gaussian model, aims to enhance the precision and reliability of TOF estimation, aiming to reduce the influence of noise interference. The algorithm combines an improved Self-Adaptive Differential Evolution (SHADE) algorithm based on successful historical records with an Extended Kalman Filter (EKF). The improved SHADE algorithm controls the degree of mutation strategy greediness during the mutation operation based on the number of iterations, thereby enhancing the algorithm’s iteration speed. Then, the obtained solution is used as the initial value for the EKF to estimate the model parameters, thus addressing the issue of EKF’s dependency on accurate initial values to obtain precise outputs. Through simulation and experimental measurements of ultrasonic oxygen concentration, several commonly used parameter estimation algorithms are compared with the proposed SHADE-EKF algorithm. Results demonstrate that the SHADE-EKF algorithm exhibits superior performance in estimating the TOF of ultrasonic waves.

Deep Reinforcement Learning-based Collaborative Multi-UAV Coverage Path Planning

Abstract The coverage path planning problem has gained significant attention in research due to its wide applicability and practical value in various fields such as logistics and distribution, smart homes, and unmanned vehicles. This paper focuses on studying the coverage path planning problem under multi-UAV collaboration to maximize the coverage of the mission area within a given time. To address this problem, we propose a multi-objective optimization model and reformulate it with the framework of Decentralized Partially Observable Markov Decision Process (Dec-POMDP). We then employ a multi-agent deep reinforcement learning (MADRL) method to solve the problem. Specifically, we introduce the ε—Multi-Agent Twin Delayed Deep Deterministic Policy Gradient (ε—MADT3), which incorporates an exploration coefficient based on MATD3. This coefficient gradually decays with the number of iterations, allowing for a balance between exploration and exploitation. Numerous simulation results demonstrate that ε—MADT3 outperforms the baseline algorithm in terms of coverage rate and number of collisions.

Research on precise lithium battery state of charge estimation method based on CALSE-LSTM model and pelican algorithm

This paper presents an innovative fusion model called “CALSE-LSTM,” which integrates Convolutional Neural Networks (CNNs), Long Short-Term Memory Networks (LSTMs), self-attention mechanisms, and squeeze-and-excitation attention mechanisms to optimize the estimation accuracy of the State of Charge (SoC). The model incorporates battery historical data as input and employs a dual-attention mechanism based on CNN-LSTM to extract diverse features from the input data, thereby enhancing the model's ability to learn hidden information. To further improve model performance, we fine-tune the model parameters using the Pelican algorithm. Experiments conducted under Urban Dynamometer Driving Schedule (UDDS) conditions show that the CALSE-LSTM model achieves a Root Mean Squared Error (RMSE) of only 1.73 % in lithium battery SoC estimation, significantly better than GRU, LSTM, and CNN-LSTM models, reducing errors by 31.9 %, 31.3 %, and 15 %, respectively. Ablation experiments further confirm the effectiveness of the dual-attention mechanism and its potential to improve SoC estimation performance. Additionally, we validate the learning efficiency of CALSE-LSTM by comparing model training time with the number of iterations. Finally, in the comparative experiment with the Kalman filtering method, the model in this paper significantly improved its performance by incorporating power consumption as an additional feature input. This further verifies the accuracy of CALSE-LSTM in estimating the State of Charge (SoC) of lithium batteries.

A deep learning-based convolutional spatiotemporal network proxy model for reservoir production prediction

Accurate production prediction is crucial in the field of reservoir management and production optimization. Traditional models often struggle with the complexities of nonlinear relationships and high-dimensional data, which hinders their ability to capture the variability of the production process efficiently and results in time-consuming calculations. To overcome these limitations, this paper introduces an innovative proxy modeling technique employing a convolutional spatiotemporal neural network. This method utilizes convolutional neural networks to extract spatial features from high-dimensional data, while the Transformer is used to model and predict complex temporal dynamics in production. To validate the effectiveness of the proposed proxy model, two case studies involving four injection and nine production wells within two-dimensional (2D) and three-dimensional (3D) non-homogeneous reservoirs were conducted, with the R2 coefficient serving as the primary evaluation metric. As the number of training iterations and data volume increase, the proxy model demonstrates rapid convergence. In tests conducted on the 2D and 3D datasets, the average R2 value exceeded 0.96 and 0.94. These results confirm the accuracy and stability of the proxy model. It also shows that the proxy model can accurately describe the geological and fluid seepage characteristics of the reservoir, which in turn can achieve a highly accurate match with the real data. In addition, the computational time is reduced by two orders of magnitude compared to traditional models. Compared with the long short-term memory method, the accuracy of the prediction results is increased by 30%, which greatly enhances efficiency and accuracy. To some extent, the presented proxy model can provide some guidance for the efficient history match of production data.

Automatic segmentation of the maxillary sinus on cone beam computed tomographic images with U-Net deep learning model

BackgroundMedical imaging segmentation is the use of image processing techniques to expand specific structures or areas in medical images. This technique is used to separate and display different textures or shapes in an image. The aim of this study is to develop a deep learning-based method to perform maxillary sinus segmentation using cone beam computed tomography (CBCT) images. The proposed segmentation method aims to provide better image guidance to surgeons and specialists by determining the boundaries of the maxillary sinus cavities. In this way, more accurate diagnoses can be made and surgical interventions can be performed more successfully.MethodsIn the study, axial CBCT images of 100 patients (200 maxillary sinuses) were used. These images were marked to identify the maxillary sinus walls. The marked regions are masked for use in the maxillary sinus segmentation model. U-Net, one of the deep learning methods, was used for segmentation. The training process was carried out for 10 epochs and 100 iterations per epoch. The epoch and iteration numbers in which the model showed maximum success were determined using the early stopping method.ResultsAfter the segmentation operations performed with the U-Net model trained using CBCT images, both visual and numerical results were obtained. In order to measure the performance of the U-Net model, IoU (Intersection over Union) and F1 Score metrics were used. As a result of the tests of the model, the IoU value was found to be 0.9275 and the F1 Score value was 0.9784.ConclusionThe U-Net model has shown high success in maxillary sinus segmentation. In this way, fast and highly accurate evaluations are possible, saving time by reducing the workload of clinicians and eliminating subjective errors.

[formula omitted]: A versatile approach for unsupervised segmentation of calcium imaging data

Recent advances in calcium imaging, including the development of fast and sensitive genetically encoded indicators, high-resolution camera chips for wide-field imaging, and resonant scanning mirrors in laser scanning microscopy, have notably improved the temporal and spatial resolution of functional imaging analysis. Nonetheless, the variability of imaging approaches and brain structures challenges the development of versatile and reliable segmentation methods. Standard techniques, such as manual selection of regions of interest or machine learning solutions, often fall short due to either user bias, non-transferability among systems, or computational demand. To overcome these issues, we developed CalciSeg, a data-driven and reproducible approach for unsupervised functional calcium imaging data segmentation. CalciSeg addresses the challenges associated with brain structure variability and user bias by offering a computationally efficient solution for automatic image segmentation based on two parameters: regions’ size limits and number of refinement iterations. We evaluated CalciSeg efficacy on datasets of varied complexity, different insect species (locusts, bees, and cockroaches), and imaging systems (wide-field, confocal, and multiphoton), showing the robustness and generality of our approach. Finally, the user-friendly nature and open-source availability of CalciSeg facilitate the integration of this algorithm into existing analysis pipelines.

Modeling of interfacial multi-cracks in dissimilar laminated structures using a nodal-based Lagrange multiplier/cohesive zone approach

Recent decades have witnessed a growing interest in simulating interfacial debonding in laminated structures using cohesive zone (CZ)-based algorithms. In the present work, we develop a nodal-based Lagrange multiplier/cohesive zone (LM/CZ) approach to achieve the end with a special focus on interfacial multi-cracks in dissimilar laminated structures. The main advantages of the developed approach are four-folded: (1) being flexible for the mesh discretization of dissimilar laminated structures and compatible with various element types; (2) being computationally more efficient for dissimilar laminated structures; (3) addressing the so-called artificial compliance issue arising in intrinsic CZ modeling; (4) providing smooth transitions from uncracked to cracking states, and from cracking to contact states. In the presented approach, nodal pairs are constructed with the aid of a searching algorithm capable of dealing with matching and non-matching meshes in a unified manner. For each nodal pair, the displacement continuity is accurately enforced using LMs that are calculated in a predictor–corrector manner with a limited number of iterations. The constraints for nodal pairs are switched from LMs to cohesive forces after a defined criterion is satisfied. The non-penetration condition between interfaces is fulfilled using penalty-based contact forces in the cracking and pure contact states, leading to a smooth transition from cracking to contact states. The accuracy and effectiveness of the presented approach are validated using three benchmark tests. Finally, the capacity of the approach to describe interfacial multi-crack behaviors of dissimilar laminated structures has been exploited and demonstrated.

The traveling purchaser problem for perishable foods

This paper addresses the well-known traveling purchaser problem (TPP) considering restrictions related to perishable food, which is called the traveling purchaser problem for perishable foods (TPP-PF). In addition to the main assumptions of the capacitated TPP, the TPP-PF takes into account the release times of perishable foods at markets. In this context, a product can only be purchased at a market after it becomes available for sale. The TPP-PF also considers that the quality of perishable products decreases due to waiting on the market shelves and during transportation, and it additionally takes the deterioration cost of the foods into account. The aim of the problem is to find the best procurement and route plan for the purchaser to minimize the total transportation cost of the temperature-controlled vehicle, the damage cost of perishable foods, and the purchasing cost. Since the deterioration cost of products based on the waiting time is determined through exponential functions, the problem is formulated as a mixed-integer non-linear programming model. To find efficient results for the problem, an adaptive large neighborhood search (ALNS) algorithm is introduced with new problem-specific destroy/repair operators. Furthermore, an additional mechanism is included in the ALNS to change the direction of the search when the algorithm cannot improve the best solution after a number of iterations. In order to analyze the performance of the proposed ALNS, a new benchmark problem set is generated using a well-known TPP benchmark set. The proposed ALNS is first performed for the TPP-PF instances and compared to GUROBI and a simulated annealing algorithm. Following the TPP-PF experiments, the ALNS is carried out for the TPP instances and compared to six state-of-the-art solution approaches. The computational results show that the proposed ALNS outperforms those approaches by finding better results for almost all instances.

The efficacy of Relative Strength Index (RSI) in KLSE market trade

The Relative Strength Index (RSI) is a widely used technical indicator in stock trading because of its simple application. However, its application combined with fundamental analysis in Kuala Lumpur Stock Exchange (KLSE) is yet to be explored extensively. Hence, this study aimed to investigate the effectiveness of RSI as a predictive tool in the KLSE market. First, 39 stocks that met the set of criteria guided by fundamental soundness were identified. Trading signals are then initiated based on the RSI indicators, which are superimposed on the charts of the identified stocks. The return on investment (ROI) was then estimated and benchmarked against KLCI performance over a period of five years starting from 21st July 21, 2018. It was found that the average ROI was 3.46% against KLCI’s -24.37% over the same period of 5 years, measured between 21st July 21, 2018, 21st July 21, 2023. The average ROI improves as the number of trade iterations increases to five. The peak average ROI is approximately 22%. Technology is the top performer, recording an ROI of more than 40%. In conclusion, the combination of RSI and fundamental analysis yielded a mixed set of results. Although it outperforms KLCI, the annualised ROI is only slightly above 4%. Nevertheless, the results of this study provide valuable insights into the application of the RSI as a trading signal generator in the KLSE market.

New Parameters of the Conjugate Gradient Method to Solve Nonlinear Systems of Equations

The conjugated gradient methods can solve smooth functions with large-scale variables in the specified number of iterations for that they are highly important methods compared to concerning other iterative methods. In this paper, we propose two new conjugate gradient methods, namely the PMDL-1 and PMDL-2. However, for non-smooth functions, which are called conjugate gradient-free derivative methods depending on the projection technique. The two methods give great results compared to the basic PDL method. Moreover, we provide theorems that prove the global convergence between these two methods.

Calculation Method for Particle Self-Regulation Servo Based on Discrete Element Method

Particle Flow Code, as noncontinuous media calculation software, has found extensive applications in geotechnical engineering research. To simulate real physical processes, the commonly utilized servo-computing methods involve adjusting the boundaries to modify the model’s stress state. However, this approach alters the model’s initial boundaries, thereby compromising computational accuracy. Addressing this issue, this paper introduces a particle self-regulation servo-computing method. This method controls the internal particle self-adjustment and completes the servo through error analysis. On the basis of the error analysis of the average stress within the particle system and the servo stress during the iterative process, the method automatically calculates the change in particle size within the system, achieving rapid convergence to servo stress tolerance after finite number of iterations. Validation through uniaxial compression tests and complex slope cases indicates that this particle self-regulation servo method yields an error of less than 5% compared with conventional rigid servo methods. That is, it accurately achieves numerical simulation state control without altering the outer contours of the boundary model. The proposed computational method is applicable to servo calculations for irregular models in two or three dimensions, providing a viable approach for stress control in models under complex conditions.

Personalized rehabilitation approach for reaching movement using reinforcement learning

Musculoskeletal disorders challenge significantly the performance of many daily life activities, thus impacting the quality of life. The efficiency of the traditional physical therapy programs is limited by ecological parameters such as intervention duration and frequency, number of caregivers, geographic accessibility, as well as by subjective factors such as patient’s motivation and perseverance in training. The implementation of VR rehabilitation systems may address these limitations, but the technology still needs to be improved and clinically validated. Furthermore, current applications generally lack flexibility and personalization. A VR rehabilitation game simulation is developed, which focuses on the upper-limb movement of reaching, an essential movement involved in numerous daily life activities. Its novelty consists in the integration of a machine learning algorithm, enabling highly adaptive and patient-customized therapeutic intervention. An immersive VR system for the rehabilitation of reaching movement using a bubble popping game is proposed. In the virtual space, the patient is presented with bubbles appearing at different locations and is asked to reach the bubble with the injured limb and pop it. The implementation of a Q-learning algorithm enables the game to adjust the location of the next bubble according to the performance of the patient, represented by his kinematic characteristics. Two test cases simulate the performance of the patient during a training program of 10 days/sessions, in order to validate the effectiveness of the algorithm, demonstrated by the spatial and temporal distribution of the bubbles in each evolving scenario. The results show that the algorithm learns the patient’s capabilities and successfully adapts to them, following the reward policy dictated by the therapist; moreover, the algorithm is highly responsive to kinematic features’ variation, while demanding a reasonable number of iterations. A novel approach for upper limb rehabilitation is presented, making use of immersive VR and reinforcement learning. The simulation suggests that the algorithm offers adaptive capabilities and high flexibility, needed in the comprehensive personalization of a rehabilitation process. Future work will demonstrate the concept in clinical trials.

Self‐training with Bayesian neural networks and spatial priors for unsupervised domain adaptation in crack segmentation

AbstractThis study proposes a novel self‐training framework for unsupervised domain adaptation in the segmentation of concrete wall cracks using accumulated crack data. The proposed method incorporates Bayesian neural networks for uncertainty estimation of pseudo‐labels, and spatial priors of cracks for screening noisy labels. Experiments demonstrate that the proposed approach achieves significant improvements in F1 score. Comparing the F1 scores, Bayesian DeepLabv3+ and Bayesian U‐Net showed performance improvements of 0.0588 and 0.1501, respectively, after domain adaptation. Furthermore, the integration of Stable Diffusion for few‐shot image generation enhances domain adaptation performance by 0.0332. The proposed framework enables high‐precision crack segmentation with as few as 100 target images, which can be easily obtained at the site, reducing the cost of model deployment in infrastructure maintenance. The study also investigates the optimal number of iterations for domain adaptation based on the uncertainty score, providing insights for practical implementation. The proposed method contributes to the development of efficient and automated structural health monitoring using AI.

Enhancing convergence speed in sparse signal denoising: the APFISTA algorithm

Among numerous first-order algorithms, the Fast Iterative Shrinkage-Thresholding Algorithm, known as FISTA, is renowned for its convergence speed of O ( 1 k 2 ) in terms of the objective function value, where k denotes the number of iterations. Additionally, various improvements to FISTA have been proposed in the literature. Among them, the convergence rate of a parameterized FISTA (PFISTA) proposed by Liang, Luo and Schonlieb [SIAM J Sci Comput. 2022:44(3):A1069–A1091] is obviously faster than that of the original FISTA, which can reach o ( 1 k 2 ) convergence rate. Building upon the idea of parameterization, we introduce the fully parameterized APFISTA for complete parameterization of the inertia term, aiming to enhance the current situation of partially parameterized inertia terms. We establish the convergence speed of its objective function value and the sequence generated by the algorithm. Finally, we apply the proposed method to solve the least squares problem and linear inverse problems. The obtained numerical results illustrate the practical behavior and theoretical analysis of the proposed approach.

Numerical Analysis of a Time-Simultaneous Multigrid Solver for Stabilized Convection-Dominated Transport Problems in 1D

This work focuses on the solution of the convection–diffusion equation, especially for small diffusion coefficients, employing a time-simultaneous multigrid algorithm, which is closely related to multigrid waveform relaxation. For discretization purposes, linear finite elements are used while the Crank–Nicolson scheme acts as the time integrator. By combining all time steps into a global linear system of equations and rearranging the degrees of freedom, a space-only problem is formed with vector-valued unknowns for each spatial node. The generalized minimal residual method with block Jacobi preconditioning can be used to numerically solve the (spatial) problem, allowing a higher degree of parallelization in space. A time-simultaneous multigrid approach is applied, utilizing space-only coarsening and the aforementioned solution techniques for smoothing purposes. Numerical studies analyze the iterative solution technique for 1D test problems. For the heat equation, the number of iterations stays bounded independently of the number of time steps, the time increment, and the spatial resolution. However, convergence issues arise in situations where the diffusion coefficient is small compared to the grid size and the magnitude of the velocity field. Therefore, a higher-order variational multiscale stabilization is used to improve the convergence behavior and solution smoothness without compromising its accuracy in convection-dominated scenarios.

Novel Integer Division for Embedded Systems: Generic Algorithm Optimal for Large Divisors

The integer Constant Division (ICD) is the type of integer division in which the divisor is known in advance, enabling pre-computing operations to be included. Therefore, it can be more efficient regarding computing resources and time. However, most ICD techniques are restricted by a few values or narrow boundaries for the divisor. On the other hand, the main approaches of the division algorithms, where the divisor is variable, are digit-by-digit and convergence methods. The first techniques are simple and have less sophisticated conversion logic for the quotient but also have the problem of taking significantly long latency. On the contrary, the convergence techniques rely on multiplication rather than subtraction. They estimate the quotient of division providing the quotient with minimal latency at the expense of precision. This article suggests a precise, generic, and novel integer division algorithm based on sequential recursion with fewer iterations. The suggested methodology relies on extracting the division results for non-powers-of-two divisors from those for the closest power-of-two divisors, which are obtained simply using the right bit shifting. To the authors’ best knowledge of the state-of-the-art, the number of iterations in the recurrent variable division is half the divisor bit size, and the Sweeney, Robertson, and Tocher (SRT) division, which is named after its developers, involves <i>log</i><sub>2</sub>(n) iterations. The suggested algorithm has an [(m/(n-1))-1] number of recursive iterations, where m and n are the number of bits of the dividend and the divisor, respectively. The design is simulated in the Vivado tool for validation and implemented with a Zynq UltraScale FPGA. The technique performance depends on the number of nested divisions and the size of a LUT. The two factors change according to the value of the divisor. Nevertheless, the size of the LUT is proportional to the range and the number of bits of the divisor. Furthermore, the equation that controls the number of nested blocks is illustrated in the manuscript. The proposed technique applies to both constant and variable divisors with a compact hardware area in the case of constant division. The hardware implementation of constant division has unlimited values for dividends and divisors with a compact hardware area in the case of large divisors. However, using the design in the hardware implementation of variable division is up to 64-bit dividend and 12-bit divisor. The result analysis demonstrates that this algorithm is more efficient for constant division for large numbers.