scholarly journals Fractional Newton-Raphson Method

2021 ◽  
Vol 8 (1) ◽  
pp. 1-13
Author(s):  
A. Torres-Hernandez ◽  
F. Brambila-Paz
Keyword(s):  
Fractional Calculus ◽  
Iterative Method ◽  
Complex Numbers ◽  
Initial Condition ◽  
The Real ◽  
Complex Roots ◽  
Newton Raphson ◽  
Roots Of A Polynomial ◽  
Raphson Method

The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n, with n ∈ N. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real initial condition is taken. In the present work, we explain an iterative method that is created using the fractional calculus, which we will call the Fractional Newton-Raphson (F N-R) Method, which has the ability to enter the space of complex numbers given a real initial condition, which allows us to find both the real and complex roots of a polynomial unlike the classical Newton-Raphson method.

scholarly journals Visualising Complex Polynomials: A Parabola Is but a Drop in the Ocean of Quadratics

2018 ◽  
Vol 10 (6) ◽  
pp. 91
Author(s):  
Harry Wiggins ◽  
Ansie Harding ◽  
Johann Engelbrecht
Keyword(s):  
Complex Function ◽  
Three Dimensional ◽  
Complex Numbers ◽  
Complex Polynomials ◽  
Singular Case ◽  
Hyperbolic Paraboloid ◽  
Complex Roots ◽  
Roots Of Polynomials ◽  
Complex Coefficients ◽  
Roots Of A Polynomial

One of the problems encountered when teaching complex numbers arises from an inability to visualise the complex roots, the so-called "imaginary" roots of a polynomial. Being four dimensional, it is problematic to visualize graphs and roots of polynomials with complex coefficients in spite of many attempts through centuries. An innovative way is described to visualize the graphs and roots of functions, by restricting the domain of the complex function to those complex numbers that map onto real values, leading to the concept of three dimensional sibling curves. Using this approach we see that a parabola is but a singular case of a complex quadratic.  We see that sibling curves of a complex quadratic lie on a three-dimensional hyperbolic paraboloid. Finally, we show that the restriction to a real range causes no loss of generality.

scholarly journals Complex roots of polynomials and their computation with the help of Scientific Calculators

BIBECHANA ◽  
2012 ◽  
Vol 9 ◽  
pp. 18-27
Author(s):  
Mohd Yusuf Yasin
Keyword(s):  
Number System ◽  
Complex Numbers ◽  
Real Numbers ◽  
Engineering Technology ◽  
The Real ◽  
Complex Roots ◽  
Wide Range ◽  
Range Of Functions ◽  
Imaginary Number

Real numbers are something which are associated with the practical life. This number system is one dimensional. Situations arise when the real numbers fail to provide a solution. Perhaps the Italian mathematician Gerolamo Cardano is the first known mathematician who pointed out the necessity of imaginary and complex numbers. Complex numbers are now a vital part of sciences and are used in various branches of engineering, technology, electromagnetism, quantum theory, chaos theory etc. A complex number constitutes a real number along with an imaginary number that lies on the quadrature axis and gives an additional dimension to the number system. Therefore any computation based on complex numbers, is usually complex because both the real and imaginary parts of the number are to be simultaneously dealt with. Modern scientific calculators are capable of performing on a wide range of functions on complex numbers in their COMP and CMPLX modes with an equal ease as with the real numbers. In this work, the use of scientific calculators (Casio brand) for efficient determination of complex roots of various types of equations is discussed. DOI: http://dx.doi.org/10.3126/bibechana.v9i0.7148 BIBECHANA 9 (2013) 18-27

An iterative method for generating kinematically feasible interference-free robot trajectories

Robotica ◽  
1989 ◽  
Vol 7 (2) ◽  
pp. 119-127 ◽  
Author(s):  
R. O. Buchai ◽  
D. B. Cherchas
Keyword(s):  
Iterative Method ◽  
Quantitative Measure ◽  
Penalty Functions ◽  
Initial Estimate ◽  
Interference Constraints ◽  
Robot Trajectory ◽  
Point Motion ◽  
Newton Raphson ◽  
Point To Point ◽  
Raphson Method

SUMMARYThis paper proposes a method for finding an optimal geometric robot trajectory to perform a specified point-to-point motion without violating joint displacement limits or interference constraints. The problem is discretised, and a quantitative measure of interference is proposed. Constraint violations are represented by exterior penalty functions, and the problem is solved by iteratively improving an initial estimate of the trajectory. This is accomplished by numerically minimizing a cost functional using a modified Newton–Raphson method.

scholarly journals A New Accurate and Efficient Iterative Numerical Method for Solving the Scalar and Vector Nonlinear Equations: Approach Based on Geometric Considerations

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Grégory Antoni
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
Accurate Solution ◽  
Extended Version ◽  
Root Finding ◽  
Newton Raphson ◽  
Stationary Type ◽  
Raphson Method

This paper deals with a new numerical iterative method for finding the approximate solutions associated with both scalar and vector nonlinear equations. The iterative method proposed here is an extended version of the numerical procedure originally developed in previous works. The present study proposes to show that this new root-finding algorithm combined with a stationary-type iterative method (e.g., Gauss-Seidel or Jacobi) is able to provide a longer accurate solution than classical Newton-Raphson method. A numerical analysis of the developed iterative method is addressed and discussed on some specific equations and systems.

scholarly journals Deprived of Second Derivative Iterated Method for Solving Nonlinear Equations

2021 ◽  
Vol 58 (2) ◽  
pp. 39-44
Author(s):  
Umair Khalid Qureshi ◽  
Sanaullah Jamali ◽  
Zubair Ahmed Kalhoro ◽  
Guan Jinrui
Keyword(s):  
Applied Sciences ◽  
Iterative Method ◽  
Graphical Representation ◽  
Linear Equations ◽  
Numerical Results ◽  
Second Derivative ◽  
Practical Applications ◽  
Non Linear ◽  
Newton Raphson ◽  
Raphson Method

Non-linear equations are one of the most important and useful problems, which arises in a varied collection of practical applications in engineering and applied sciences. For this purpose, in this paper has been developed an iterative method with deprived of second derivative for the solution of non-linear problems. The developed deprived of second derivative iterative method is convergent quadratically, and which is derived from Newton Raphson Method and Taylor series. The numerical results of the developed method are compared with the Newton Raphson Method and Modified Newton Raphson Method. From graphical representation and numerical results, it has been observed that the deprived of second derivative iterative method is more appropriate and suitable as accuracy and iteration perception by the valuation of Newton Raphson Method and Modified Newton Raphson Method for estimating a non-linear problem. 

scholarly journals NUMERICAL ITERATIVE METHOD OF OPEN METHODS WITH CONVERGE CUBICALLY FOR ESTIMATING NONLINEAR APPLICATION EQUATIONS

2021 ◽  
Author(s):  
Umair Khalid Qureshi
Keyword(s):  
Iterative Method ◽  
Newton Method ◽  
Numerical Technique ◽  
Classical Problem ◽  
Practical Application ◽  
Single Root ◽  
Modified Newton Method ◽  
Newton Raphson ◽  
Engineering Physics ◽  
Raphson Method

Finding the single root of nonlinear equations is a classical problem that arises in a practical application in Engineering, Physics, Chemistry, Biosciences, etc. For this purpose, this study traces the development of a novel numerical iterative method of an open method for solving nonlinear algebraic and transcendental application equations. The proposed numerical technique has been founded from Secant Method and Newton Raphson Method, and the proposed method is compared with the Modified Newton Method and Variant Newton Method. From the results, it is pragmatic that the developed numerical iterative method is improving iteration number and accuracy with the assessment of the existing cubic method for estimating a single root nonlinear application equation.

scholarly journals DEVELOPMENT OF NEW ITERATIVE SCHEME FOR SOLVING NON-LINEAR EQUATIONS

2021 ◽  
Author(s):  
Tusar singh ◽  
Dwiti Behera
Keyword(s):  
Iterative Method ◽  
Newton’S Method ◽  
Newton's Method ◽  
Iterative Scheme ◽  
Linear Equations ◽  
Quadrature Rule ◽  
Modified Newton’S Method ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations

Within our study a special type of 〖iterative method〗^ω is developed by upgrading Newton-Raphson method. We have modified Newton’s method by using our newly developed quadrature rule which is obtained by blending Trapezoidal rule and open type Newton-cotes two point rule. Our newly developed method gives better result than the Newton’s method. Order of convergence of our newly discovered quadrature rule and iterative method is 3.

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