Newton Interpolation Method Research Articles

On Newton and Lagrange Interpolation Method for first order ordinary differential equations

On Newton and Lagrange Interpolation Method for first order ordinary differential equations

An improved two-beat deadbeat synchronous predictive current control strategy for MMC based on Newton interpolation method

An improved two-beat deadbeat synchronous predictive current control strategy for MMC based on Newton interpolation method

AFL++: A Vulnerability Discovery and Reproduction Framework

Directed greybox fuzzing can mainly be used for vulnerability mining and vulnerability replication. However, there are still some issues with existing directional fuzzing tools. One is that after providing problematic changes or patches, it is not possible to quickly target and discover the problem. Secondly, it is difficult to break through the magic byte path, making it difficult to mine deep vulnerabilities. This article proposes a new vulnerability mining and repair framework: American Fuzz Lop Plus (AFL++). Firstly, we utilize alias analysis to enhance inter-procedural control flow graphs and redefine the distance calculation formula to obtain more accurate distances. Secondly, the Newton interpolation method is used for the energy initialization of each seed to prevent test cases from being filtered out due to low energy. A heuristic energy scheduling algorithm is proposed to judiciously schedule the energy of seeds. During the path exploration phase, by adjusting the seed energy, shorter-distance seeds quickly reach the target; with increasing time, seeds tend to explore deeper paths. We then represent the symbolic distance by the number of instructions passed to reach the target and investigate the shortest path search strategy to achieve path pruning, alleviating the problem of path explosion. Finally, based on the above methods, we implement the AFL++ prototype system, integrating directed greybox fuzzing with symbolic execution technology for vulnerability discovery. By interleaving directed symbolic execution and directed greybox fuzzing, the efficiency of vulnerability discovery and reproduction is effectively enhanced.

NUMERICAL ANALYSIS OF HOME OWNERSHIP LOANS BANK INTEREST RATES IN INDONESIA WITH NEWTON'S INTERPOLATION METHOD

The demand of the Indonesian society to own homes and properties is increasing along with the growth of Indonesia's population. This has led to an increase in population density, causing property prices to rise. The way to own property or a house in accordance with monthly income is by using bank housing loans. Three Indonesian banks renowned for housing loan applications, namely BTN, Mandiri, and BSI, were selected as samples in this study. These three banks have their own advantages and different bank interest rates. Therefore, this research was created as a tool for consumers to make decisions by considering the advantages obtained when applying for a loan at one of the three banks. This study employs the Newton's interpolation method to generate formulas that can help solve consumer problems. The results of this study generally indicate that Mandiri bank has an advantage in terms of lower installment costs compared to BTN and BSI.

Two-grid finite element method with an H2N2 interpolation for two-dimensional nonlinear fractional multi-term mixed sub-diffusion and diffusion wave equation

<abstract><p>In this paper, we studied the two-grid method (TGM) for two-dimensional nonlinear time fractional multi-term mixed sub-diffusion and diffusion wave equation. A fully discrete scheme with the quadratic Hermite and Newton interpolation (H2N2) method was considered in the temporal direction and the expanded finite element method is used to approximate the spatial direction. In order to reduce computational time, a dual grid method based on Newton iteration was constructed with order $ \alpha\in(0, 1) $ and $ \beta\in(1, 2) $. The global convergence order of the two-grid scheme reaches $ O(\tau^{3-\beta}+h^{r+1}+H^{2r+2}) $, where $ \tau $, $ H $ and $ h $ are the time step size, coarse grid mesh size and fine grid mesh size, respectively. The error estimation and stability of the fully discrete scheme were derived. Theoretical analysis shows that the two grid algorithms maintain asymptotic optimal accuracy while saving computational costs. In addition, numerical experiments further confirmed the theoretical results.</p></abstract>

Three-state Variable Step Perturbation Observation MPPT Algorithm Based on Power Prediction

In view of the application and research status of maximum power point tracking technology in photovoltaic power generation system, an improved disturbance observation MPPT method with variable step size and no oscillation at steady state is proposed in this paper. The method combines power prediction disturbance method and constant voltage method. Firstly, two reasons for power loss caused by traditional disturbance observation method are analyzed, which are disturbance misjudgment and steady state oscillation respectively. In order to reduce power loss caused by disturbance misjudgment and steady state oscillation, the three-point function sampling model based on Newton interpolation method is used to reduce disturbance misjudgment respectively, and a new variable step size factor is proposed to realize fast tracking of maximum power point through variable step size. And when the steady state is reached, the disturbance step size is immediately reduced to achieve a small shock output, so as to improve the efficiency of the whole system. Finally, the photovoltaic system model and experimental platform are built to track and simulate the maximum power point. The results show that the improved disturbance observation method can not only improve the disturbance misjudgment, but also achieve stable tracking of the maximum power point.

Securing web documents by using piggybacked framework based on Newton's forward interpolation method

The modern telecommunication system that transfers data over the web requires a secure channel so that integrity, authentication, and confidentiality of data are ensured. To achieve this, the SSL/TLS protocol of the transport layer provides end-to-end security to transfer data without any intrusion. But this security fails due to vulnerabilities reported in the last few years on SSL/TLS not ignorable which makes the data communication process vulnerable. The handshake protocol used by SSL/TLS decides a common session key to share the message among the communicating nodes. The common key remains the same in a session to encrypt entire data payload. If a hacker breaks into the session and accesses the key, then the entire session would be compromised. Therefore, there is a need for a mechanism that ensures the proper key exchanges so that the messages transferred during a session uses different keys for encryption and decryption process. This is achieved by implementing the key exchange mechanism using Newton's interpolation method which is used to generate a polynomial function that derives the key for the ongoing communications. The paper represents the result of the research conducted and also recommends a few changes to the existing key exchange mechanism.

ESA-FedGNN: Efficient secure aggregation for federated graph neural networks.

Graph Neural Network (GNN) architecture is a state-of-the-art model, which can obtain complete node embedding features and rich data information by aggregating the information of nodes and neighbors. Therefore, GNNs are widely used in electronic shopping, drug discovery (especially for the treatment of COVID-19) and other fields, promoting the explosive development of machine learning. However, user interaction, data sharing and circulation are highly sensitive to privacy, and centralized storage can lead to data isolation. Therefore, Federated Learning with high efficiency and strong security and privacy enhancement technology based on secure aggregation can improve the security dilemma faced by GNN. In this paper, we propose an Efficient Secure Aggregation for Federated Graph Neural Network(ESA-FedGNN), which can efficiently reduce the cost of communication and avoid computational redundancy while ensuring data privacy. Firstly, a novel secret sharing scheme based on numerical analysis is proposed, which employs Fast Fourier Transform to improve the computational power of the neural network in sharing phase, and leverages Newton Interpolation method to deal with the disconnection and loss of the client in reconstruction phase. Secondly, a regular graph embedding based on geometric distribution is proposed, which optimizes the aggregation speed by using data parallelism. Finally, a double mask is adopted to ensure privacy and prevent malicious adversaries from stealing model parameters. We achieve improvements compared to in state-of-the-art works. This research helps to provide security solutions related to the practical development and application of privacy-preserving graph neural network technology.

Investigation of Novel Piecewise Fractional Mathematical Model for COVID-19

The outbreak of coronavirus (COVID-19) began in Wuhan, China, and spread all around the globe. For analysis of the said outbreak, mathematical formulations are important techniques that are used for the stability and predictions of infectious diseases. In the given article, a novel mathematical system of differential equations is considered under the piecewise fractional operator of Caputo and Atangana–Baleanu. The system is composed of six ordinary differential equations (ODEs) for different agents. The given model investigated the transferring chain by taking non-constant rates of transmission to satisfy the feasibility assumption of the biological environment. There are many mathematical models proposed by many scientists. The existence of a solution along with the uniqueness of a solution in the format of a piecewise Caputo operator is also developed. The numerical technique of the Newton interpolation method is developed for the piecewise subinterval approximate solution for each quantity in the sense of Caputo and Atangana-Baleanu-Caputo (ABC) fractional derivatives. The numerical simulation is drawn against the available data of Pakistan on three different time intervals, and fractional orders converge to the classical integer orders, which again converge to their equilibrium points. The piecewise fractional format in the form of a mathematical model is investigated for the novel COVID-19 model, showing the crossover dynamics. Stability and convergence are achieved on small fractional orders in less time as compared to classical orders.

Oscillatory, crossover behavior and chaos analysis of HIV-1 infection model using piece-wise Atangana–Baleanu fractional operator: Real data approach

There are many fatal diseases which are caused by virus. Different types of viruses cause different infections. One of them is HIV-1 infection which caused by retrovirus. HIV-1 infection is a hazardous disease that can lead to cancer, AIDS, and other serious illnesses. Several mathematical models have been proposed in the field and examined using various methods. In this manuscript, the newly suggested piece-wise (PW) Atangana–Baleanu (AB) fractional operator is used to examine HIV-1 infection. Some theorems related to the existence of the solution to the examined model are proved through fixed point results. The Ulam–Hyers (UH) stability and its different forms are presented for the proposed PW HIV-1 infection model. The considered model’s numerical results are attained via the Newton interpolation method. The results are graphically illustrated via MATLAB software to show the behavior of the considered model. Oscillatory and complex dynamics are obtained for some fractional orders and show the crossover behavior of the proposed model. The model’s simulation of infected class is fitted with the real data taken for six different countries. It proves the validity and accuracy of the suggested approach.

Modified Newton-residual interpolation for division of focal plane polarization image demosaicking.

With the improvement of semiconductor processing technology, polarization sensors using division of focal plane have gradually become the mainstream method of polarization imaging. Similar to the color restoration method of the Bayer array sensor, the spatial information of polarized image is also recovered through the polarization demosaicking algorithm. In this paper, we propose a new modified Newton-residual interpolation polarization image demosaicking algorithm based on residual interpolation, which is suitable for a monochrome or color polarization filter array. First, we use the modified Newton interpolation method to generate edge-sensitive guiding images. Then, we carry out the improvement of the guide process during the residual interpolation by performing variance statistics on the local window image in the guiding process, so that the edges and flat image blocks have different guiding weights. Finally, we obtain edge-preserving results by applying these two improvements, which reduces the zipper effect and edge confusion. We compare the results of various algorithms on experimental data, demonstrating that our algorithm has impactful improvements in the evaluation metrics based on the ground-truth images.

Research on the maximum power point tracking method of photovoltaic based on Newton interpolation-assisted particle swarm algorithm

Abstract Solar energy has attracted a lot of attention because it is clean and has no pollution. However, due to the partially shaded condition, the photovoltaic array cannot work uniformly at the maximum power point, resulting in a large power loss. To improve this problem, the research of the maximum power point tracking (MPPT) algorithm is discussed by scholars. In this paper, an improved particle swarm optimization (PSO) algorithm is proposed to achieve the goal of MPPT, which uses Newton interpolation-assisted conventional PSO. After tracking to the maximum power point, the Newton interpolation method is used to calculate the maximum power point, reduce the number of iterations of the conventional PSO algorithm and reduce the steady-state oscillation. The simulation is carried out in MATLAB®/Simulink® and compared with conventional PSO. The results show that the improved PSO has better tracking accuracy and speed than the conventional algorithm, and the initial tracking speed is increased by >30%.

Profitability prediction in thermal power enterprise based on the improved system dynamics model

This paper tries to improve the system dynamics model and to establish the model of the thermal power enterprise profitability by using Newton interpolation method to optimize the nonlinear function, MATLAB to fitting equation and data analysis; and through the VENSIM to present a simulation. The model is dissertated and validated by some thermal power enterprise's financial data. This model can provide enterprises with management decision-making reference.

Improved variable scale-convex-peak method for weak signal detection

Based on the rectification method of detectable domain and elimination method of blind domain, the variable scale-convex-peak method for the identification frequency of weak signal is improved. For the initial phase of weak signal to be detected, the analytic expression of chaotic threshold is obtained by using the stochastic Melnikov method. The influence of phase on chaotic threshold is clarified, which leads to that the frequency of weak signal can be identified. Specifically, within a period, the initial phase can be divided into the detectable domain and the blind domain. In the detectable domain, when the frequency identification deviates, the rectification method of detectable domain is introduced. Specifically, the Newton interpolation method is used to give the calculation formula to rectify the deviation, which improves the accuracy of frequency identification. In the blind domain, the elimination method of blind domain is given by constructing the detection equations. The feasibility of the improved variable scale-convex-peak method is verified by numerical simulation and circuit experiment. Furthermore, by comparing the identified frequency value with the theoretical fault frequency value, the fault location of the wheelset bearing of the high-speed train is determined. The improved variable scale-convex-peak method is applied when the initial phase is in the frequency detectable domain or the blind domain, respectively.

Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolation

Numerical approach of two-derivative Runge-Kutta type method with three-stage fifth-order (TDRKT3(5)) is developed and proposed for solving a special type of third-order delay differential equations (DDEs) with constant delay. An algorithm based on Newton interpolation and hybrid with the TDRKT method is built to approximate the solution of third-order DDEs. In this paper, three-stage fifth-order called TDRKT3(5) method with single third derivative and multiple evaluations of the fourth derivative is highlighted to solve third-order pantograph type delay differential equations directly with the aid of the Newton interpolation method. Stability analysis of TDRKT3(5) method is investigated. The numerical experiments illustrate high efficiency and validity of the new method for solving a special class of third-order DDEs and some future works are recommended by extending proposed method to solve fractional and singularly perturbed delay differential equations.

New correlation features for dissolved gas analysis based transformer fault diagnosis based on the maximal information coefficient

Online monitoring of gases dissolved in transformer oil is widely applied. Improving the performance of dissolved gas analysis (DGA)-based fault diagnosis methods by exploring new features of time-series data has become an appealing topic. In this study, a new type of correlation features between characteristic gases was extracted from time-series data based on the maximal information coefficient (MIC), and a fuzzy inference system was established. After the introduction of the principle of the MIC and a method for calculating the MIC-based correlation features, the dominant symptom features that can be used to classify fault types were extracted through the receiver operating characteristic curve. Then, fuzzy rules were learnt, and a fuzzy inference system was designed. In addition, to improve the feasibility of the method, the Newton interpolation method was used for adaptation to the existing sampling cycle. The diagnostic results of the test data show that the proposed method has excellent performance and outperforms some prevailing traditional rule-based methods as well as some artificial intelligent methods. The results also show that by exploring new correlation features from time-series data based on the MIC, the performance of DGA-based methods can be improved.

Feasibility Study of Hydro Power Plant (HPP) Lubuak Gadang Sangir South Solok

The feasibility study is one of the principal documents in building a hydropower plant consisting of technical, economic, and financial aspects. Contained technical studies on civil, mechanical, and electrical. This requires data on hydrologic, geology, land contours, river discharge, water catchment areas, and so on. Economic and financial studies include cost and financial parameters such as; BEP, IRR, NVP, BCR, and others. The installed capacity of a hydropower plant is given in optimization based on the Flow Duration Curve (FDC) and the Capacity Factor (CF) used the Newton Interpolation Method. The results showed that the installed power capacity was 11.99 MW. The water discharge was 31.603 m3/secs and the effective head was 37.5 meters. Annual income is around IDR 103.026 billion. Finally, HPP Lubuak Gadang is technically, economically, and financially feasible, so it is feasible to carry out the next process.

A Variable Threshold Image Secret Sharing Method

Image secret sharing has been widely discussed in recent years because of its high security. The threshold variable image secret sharing method is a hot research topic recently. The Lagrange interpolation method is easy to establish. Therefore, most of the existing secret sharing schemes are based on Lagrange interpolation polynomials. However, when the secret is updated, the existing secret sharing scheme needs to re-establish the polynomial, and the original computing resources cannot be utilized. When the cheater is found, it is not convenient to add or delete participants flexibly, resulting in a large waste of computer resources. Therefore, an image secret sharing method with variable threshold based on Newton interpolation method is proposed, which can reduce the computational complexity of the system and the amount of repeated computation. The experimental results show that the method is superior when the threshold is changed.

Successive linear Newton interpolation methods for solving the large-scale nonlinear eigenvalue problems

We present the successive linear Newton interpolation method for solving the large-scale nonlinear eigenvalue problems, establish locally linear convergence, and give the corresponding convergence factor of the method in terms of the left and right eigenvectors in this paper. To speed up the convergence rate, we develop the modified successive linear Newton interpolation method which updates the pole simultaneously. In addition, we propose the inexact versions of the (modified) successive linear Newton interpolation method to reduce the computational cost and analyze the convergence properties. Numerical results demonstrate the effectiveness of our proposed methods.

A novel approach for computation of cosine function

Objective of trigonometric function approximation in digital systems are faster computation in less number of clock cycles, optimising hardware resources, accuracy in more number of bits, etc. This study proposes a novel method for cosine function computation and respective FPGA-based architecture. A triangle is presumably located in the first quadrant of a circle with unit radius whose one vertex is the centre, other two vertices touches the perimeter. Using the area of the triangle, it is observed that the y coordinate of the third vertex of the triangle is the sine value. The error is the difference between arch length and side length. Newton's interpolation method is used to formulate the error approximation function. This method is synthesised on Xilinx Spartan 3 xc3s200-5ft256 FPGA kit. The proposed method gives accuracy up to 14 bits or more in 96% cases in 11 clock cycles only at maximum speed of 89.977 MHz.