1,937 Results Found

Dynamic mode decomposition (DMD) is a powerful data-driven tool for analyzing complex systems that has gained significant attention in various scientific and engineering disciplines. It is suitable for the analysis of flow structures in numerical and...

Cryptography is the process of transforming data so that only the recipient of the message can read it. It uses an algorithm and a key to convert an input into an encrypted output. In this study, we introduce a novel method for protecting readable me...

The aim of this paper is to investigate experimentally and to present visually the dynamics of the processes in which in the standard Newton’s root-finding method the classic derivative is replaced by the fractional Riemann–Liouville or C...

Bairstow’s method employs synthetic division to express a polynomial $p\left(x\right)$ of degree n in the form $p\left(x\right)=q\left(x\right)(x^2+Bx+C)+R(B,C)x+S(B,C)$, where $q\left(x\right)$ is the quotient polynomial of degree $n-2$, and $R(B,C)$, $S(B,C)$ are the remainder coefficients th...

In this manuscript, by using the weight-function technique, a new class of iterative methods for solving nonlinear problems is constructed, which includes many known schemes that can be obtained by choosing different weight functions. This weight fun...

Research interest in iterative multipoint schemes to solve nonlinear problems has increased recently because of the drawbacks of point-to-point methods, which need high-order derivatives to increase the order of convergence. However, this order is no...

This paper is dedicated to the study of continuous Newton’s method, which is a generic differential equation whose associated flow tends to the zeros of a given polynomial. Firstly, we analyze some numerical features related to the root-finding metho...

Fractional calculus plays a central role in modeling memory-dependent processes and complex dynamics across various fields, including control theory, fluid mechanics, and bioengineering. This study introduces an efficient and stable fractional-order...

In this paper, a general family of n-point Newton type iterative methods for solving nonlinear equations is constructed by using direct Hermite interpolation. The order of convergence of the new n-point iterative methods without memory is 2n requirin...

In this paper, a self-accelerating type method is proposed for solving nonlinear equations, which is a modified Ren’s method. A simple way is applied to construct a variable self-accelerating parameter of the new method, which does not increase...

Finding a simple root for a nonlinear equation $f\left(x\right)=0$ , $f:I\subseteq \mathbb{R}\to \mathbb{R}$ has always been of much interest due to its wide applications in many fields of science and engineering. Newton’s method is usually applied to s...

In this paper, we obtain two iterative methods with memory by using inverse interpolation. Firstly, using three function evaluations, we present a two-step iterative method with memory, which has the convergence order 4.5616. Secondly, a three-step i...

Fractional calculus extends the conventional concepts of derivatives and integrals to non-integer orders, providing a robust mathematical framework for modeling complex systems characterized by memory and hereditary properties. This study enhances th...

The method of determination of complex dielectric permIttIvIty of loss materials at microwave frequencies (X-band) using measured amplitudes of reflection and transmission coefficients and numerical calculations is developed. Different numerical meth...

A straightforward family of one-point multiple-root iterative methods is introduced. The family is generated using the technique of weight functions. The order of convergence of the family is determined in its convergence analysis, which shows the co...

In this paper, we propose a novel blended algorithm that has the advantages of the trisection method and the false position method. Numerical results indicate that the proposed algorithm outperforms the secant, the trisection, the Newton–Raphson, the...

There is an increasing demand for numerical methods to obtain accurate approximate solutions for nonlinear models based upon polynomials and transcendental equations under both single and multivariate variables. Keeping in mind the high demand within...

Perturbation theory is systematically used to generate root finding algorithms with fourth order derivatives. Depending on the number of correction terms in the perturbation expansion and the number of Taylor expansion terms, different root finding...

A novel Newton-type n-point iterative method with memory is proposed for solving nonlinear equations, which is constructed by the Hermite interpolation. The proposed iterative method with memory reaches the order $(2^n+2^{n-1}-1+\sqrt{2^{2n+1}+2^{2n\&minu}}$...

Nonlinear phenomena occur in various fields of science, business, and engineering. Research in the area of computational science is constantly growing, with the development of new numerical schemes or with the modification of existing ones. However,...

Finding all the roots of a nonlinear equation is an important and difficult task that arises naturally in numerous scientific and engineering applications. Sequential iterative algorithms frequently use a deflating strategy to compute all the roots o...

Advanced computational methods are being applied to address traditional guidance problems, yet research is still ongoing regarding how to utilize them effectively and scientifically. A numerical root-finding method was proposed to determine the bias...

We present a novel machine learning (ML)-based method to accelerate conservative-to-primitive inversion, focusing on hybrid piecewise polytropic and tabulated equations of state. Traditional root-finding techniques are computationally expensive, part...

The new perturbation iteration method developed by Pakdemirli and co- workers are reviewed. First, applications of the method to algebraic equations are discussed and some new root-finding algorithms developed by this method are given. Next, the appl...

It is essential to solve nonlinear equations in engineering, where accuracy and precision are critical. In this paper, a novel family of iterative methods for finding the simple roots of nonlinear equations based on multiplicative calculus is introdu...

To address the problem of expensive computation in traditional two-dimensional (2D) direction of arrival (DOA) estimation, in this paper, we propose a 2D DOA estimation method based on a reduced dimension and root-finding MUSIC algorithm for nested p...

The aim of this paper is to delve into the dynamic study of the well-known Chebyshev–Halley family of iterative methods for solving nonlinear equations. Our objectives are twofold: On the one hand, we are interested in characterizing the existe...

In this paper, a family of Steffensen-type methods of optimal order of convergence with two parameters is constructed by direct Newtonian interpolation. It satisfies the conjecture proposed by Kung and Traub (J. Assoc. Comput. Math. 1974, 21, 634–651...

Nonlinear problems, which often arise in various scientific and engineering disciplines, typically involve nonlinear equations or functions with multiple solutions. Analytical solutions to these problems are often impossible to obtain, necessitating...

In this article, we construct an efficient family of simultaneous methods for finding all the distinct as well as multiple roots of polynomial equations. Convergence analysis proves that the order of convergence of newly constructed family of simulta...

In this paper, we have constructed new families of derivative-free three- and four-parametric methods with and without memory for finding the roots of nonlinear equations. Error analysis verifies that the without-memory methods are optimal as per Kun...

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal f...

There is a huge group of algorithms described in the literature that iteratively find solutions of a given equation. Most of them require tuning. The article presents root-finding algorithms that are based on the Newton–Raphson method which ite...

For applications like smart cities and autonomous driving, high-precision direction-of-arrival (DOA) estimation for 5G broadband signals is essential. A primary obstacle for existing methods is the spatial incoherence caused by multi-frequency propag...

Solving fractional-order nonlinear equations is crucial in engineering, where precision and accuracy are essential. This study introduces a novel fractional parallel technique for solving nonlinear equations. To enhance convergence, we incorporate a...

Quantum calculus can provide new insights into the nonlinear behaviour of functions and equations, addressing problems that may be difficult to tackle by classical calculus due to high nonlinearity. Iterative methods for solving nonlinear equations c...

This paper addresses the challenge of implementing Direction of Arrival (DOA) methods for indoor localization using Internet of Things (IoT) devices, particularly with the recent direction-finding capability of Bluetooth. DOA methods are complex nume...

The numerical solution of relativistic hydrodynamics equations in conservative form requires root-finding algorithms that invert the conservative-to-primitive variables map. These algorithms employ the equation of state of the fluid and can be comput...

In practical array signal processing applications, direction-of-arrival (DOA) estimation often suffers from degraded accuracy under low signal-to-noise ratio (SNR) and limited snapshot conditions. To address these challenges, we propose an off-grid D...

This paper presents two novel hybrid iterative schemes that combine Newton’s method and its variant with the Tuna Swarm Optimization (TSO) algorithm, aimed at solving complex nonlinear equations with enhanced accuracy and efficiency. Newton&rsq...

To study the acoustic characteristics of sound scattered from laminated structures such as elastic plates and shells, it is usually required to solve the Lamb waves’ dispersion equations. Many traditional root-finding methods such as bisection,...

This paper proposes a novel sparse array design and an efficient algorithm for two-dimensional direction-of-arrival (2D-DOA) estimation. By analyzing the hole distribution in coprime arrays and introducing supplementary elements, we design a Compleme...

Bilateral correlated data frequently arise in medical clinical studies such as otolaryngology and ophthalmology. Based on an equal correlation coefficient model, this paper mainly aimed to investigate the statistical inference for the odds ratio of t...

Fractional-order nonlinear equation-solving methods are crucial in engineering, where complex system modeling requires great precision and accuracy. Engineers may design more reliable mechanisms, enhance performance, and develop more accurate predict...

This paper describes an exact linearizing control approach for a distributed actuation magnetic bearing (DAMB) supporting a thin-walled rotor. The radial DAMB design incorporates a circular array of compact electromagnetic actuators with multi-coil w...

This paper presents the development of a robust sizing method to efficiently estimate and compare key performance parameters in the conceptual design stage for the two main classes of fully electric vertical take-off and landing (eVTOL) aircraft, the...

The rise of modern cryptographic protocols such as Zero-Knowledge proofs and secure Multi-party Computation has led to an increased demand for a new class of symmetric primitives. Unlike traditional platforms such as servers, microcontrollers, and de...

Orthogonal frequency division multiple access (OFDMA), which is widely used in the wireless sensor networks, allows different users to obtain different subcarriers according to their subchannel gains. Therefore, how to assign subcarriers and power to...

Interval Type-2 fuzzy systems allow the possibility of considering uncertainty in models based on fuzzy systems, and enable an increase of robustness in solutions to applications, but also increase the complexity of the fuzzy system design. Several a...

The proliferation of inverter-based distributed energy resources (IBDERs) has increased the number of control variables and dynamic interactions, leading to new grid control challenges. For stability analysis and designing appropriate protection cont...