scholarly journals Rotation intervals for a class of maps of the real line into itself

1986 ◽  
Vol 6 (1) ◽  
pp. 117-132 ◽  
Author(s):  
Michał Misiurewicz
Keyword(s):  
Newton’S Method ◽  
Real Line ◽  
Newton's Method ◽  
Continuous Case ◽  
The Real ◽  
Solving Equations

AbstractWe study a class of maps of the real line into itself which are degree one liftings of maps of the circle and have discontinuities only of a special type. This class contains liftings of continuous degree one maps of the circle, lifting of increasing mod 1 maps and some maps arising from Newton's method of solving equations. We generalize some results known for the continuous case.

scholarly journals Increasing the interval of convergence for a generalized Newton's method of solving nonlinear equations

2016 ◽  
pp. 7-12
Author(s):  
А.Н. Громов
Keyword(s):  
Continuous Function ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
The Real ◽  
Real Roots ◽  
Complex Roots ◽  
Transcendental Equations ◽  
Generalized Newton’S Method

Рассмотрен подход к построению расширения промежутка сходимости ранее предложенного обобщения метода Ньютона для решения нелинейных уравнений одного переменного. Подход основан на использовании свойства ограниченности непрерывной функции, определенной на отрезке. Доказано, что для поиска действительных корней вещественнозначного многочлена с комплексными корнями предложенный подход дает итерации с нелокальной сходимостью. Результат обобщен на случай трансцендентных уравнений. An approach to the construction of an extended interval of convergence for a previously proposed generalization of Newton's method to solve nonlinear equations of one variable. This approach is based on the boundedness of a continuous function defined on a segment. It is proved that, for the search for the real roots of a real-valued polynomial with complex roots, the proposed approach provides iterations with nonlocal convergence. This result is generalized to the case transcendental equations.

A note on the real zeros of the basic confluent hypergeometric function

1968 ◽  
Vol 64 (3) ◽  
pp. 683-686
Author(s):  
Ramadhar Mishra
Keyword(s):  
Hypergeometric Function ◽  
Newton’S Method ◽  
Newton's Method ◽  
Numerical Evaluation ◽  
Confluent Hypergeometric Function ◽  
The Real ◽  
Real Zeros ◽  
In Series

Some years back, Slater (4) discussed the approximations, based on the expansion in series, for the cases 1F1(a; b; x) = 0, when either of b and x or a and x are fixed. These approximations were based essentially on the well-known Newton's method of approximation and were helpful in the numerical evaluation of the small real zeros of the confluent hypergeometric function 1F1(a; b; x;). In this note, we deal with the corresponding problem for the basic confluent hypergeometric function 1Φ1(a; b; x;).

Optimal Power Flow Using Newton’s Method

2012 ◽  
Vol 3 (2) ◽  
pp. 167-169
Author(s):  
F.M.PATEL F.M.PATEL ◽  
◽  
N. B. PANCHAL N. B. PANCHAL
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Optimal Power

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

AN OSCILLATION FUNCTION ON THE REAL LINE

2000 ◽  
Vol 26 (1) ◽  
pp. 237
Author(s):  
Duszyński
Keyword(s):  
Real Line ◽  
The Real

DERIVATION BASES ON THE REAL LINE (I)

1982 ◽  
Vol 8 (1) ◽  
pp. 67 ◽  
Author(s):  
Thomson
Keyword(s):  
Real Line ◽  
The Real
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