Generalizations of Bernstein and Turán-Type Inequalities for the Polar Derivative of a Complex Polynomial

2019 ◽  
Vol 17 (1) ◽  
Author(s):  
Abdullah Mir
Keyword(s):  
Complex Polynomial ◽  
Polar Derivative ◽  
Turán Type Inequalities

scholarly journals Generalizations of some Zygmund-type integral inequalities for polar derivatives of a complex polynomial

2021 ◽  
Vol 110 (124) ◽  
pp. 57-69
Author(s):  
Abdullah Mir
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Integral Inequalities ◽  
Complex Polynomial ◽  
Algebraic Polynomials ◽  
Polar Derivative ◽  
Type Integral ◽  
Polar Derivatives ◽  
Derivatives Of

We prove some results for algebraic polynomials in the complex plane that relate the L-norm of the polar derivative of a complex polynomial and the polynomial under some conditions. The obtained results include several interesting generalizations of some Zygmund-type integral inequalities for polynomials and derive polar derivative analogues of some classical Bernsteintype inequalities for the sup-norms on the unit disk as well.

scholarly journals ON THE ZERO-FREE REGIONS FOR POLAR DERIVATIVE OF POLYNOMIALS WITH RESTRICTED COEFFICIENTS

2021 ◽  
pp. 127-139
Author(s):  
C. Gangadhar ◽  
P. Ramulu ◽  
G. L. Reddy ◽  
P. Venkateshwarlu
Keyword(s):  
Polar Derivative

scholarly journals Annular Bounds for the Zeros of a Polynomial

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Le Gao ◽  
N. K. Govil
Keyword(s):  
Complex Polynomial

The problem of obtaining the smallest possible region containing all the zeros of a polynomial has been attracting more and more attention recently, and in this paper, we obtain several results providing the annular regions that contain all the zeros of a complex polynomial. Using MATLAB, we construct specific examples of polynomials and show that for these polynomials our results give sharper regions than those obtainable from some of the known results.

Seismic calibration using the simplex algorithm

1989 ◽  
Vol 79 (5) ◽  
pp. 1618-1628
Author(s):  
Lee Steck ◽  
William A. Prothero
Keyword(s):  
Response Function ◽  
Degrees Of Freedom ◽  
Simplex Algorithm ◽  
Complex Polynomial ◽  
High Signal ◽  
Polynomial Representation ◽  
Important Improvement ◽  
The Time Domain ◽  
Calibration Program ◽  
Starting Model

Abstract We have modified the software of Sauter and Dorman (1986) to produce a robust and flexible calibration program that works in the frequency domain for longer and noisy calibration signals, as well as in the time domain when shorter, high signal-to-noise calibration signals may be used. The most important improvement was to replace the least squares fitting of the complex polynomial representation of the response function with the simplex fitting of the pole-zero representation of the response function. The simplex algorithm always converges to a minimum, regardless of starting model, and by fitting the poles and zeroes directly, we minimize the degrees of freedom of the solution. Typical VAX 11/750 CPU requirements are on the order of 2 to 3 minutes for both codes, with average errors less than 1 per cent in amplitude and 1° in phase.

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