Varun ..

Varun ..
University of Lucknow · Department of Mathematics and Astronomy

M.Sc. NET-JRF GATE

About

15
Publications
3,228
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
6
Citations
Citations since 2017
15 Research Items
6 Citations
20172018201920202021202220230123456
20172018201920202021202220230123456
20172018201920202021202220230123456
20172018201920202021202220230123456
Additional affiliations
January 2017 - present
University of Lucknow
Position
  • PhD Student
Description
  • I am research scholar at University of Lucknow. I am working on different types of interpolation techniques to analyse and approximate analytic and continous function in a unit disk via interpolatory polynomial. I am also interested in the applications of interpolation on the unit circle and numerically justify the works done in this direction.
Education
January 2017 - May 2022
University of Lucknow
Field of study
  • APPROXIMATION THEORY ( DIFFERENT TYPES OF INTERPOLATING POLYNOMIALS AND THEIR CONVERGENCE BEHAVIOUR)

Publications

Publications (15)
Article
Full-text available
The paper is devoted to the study of a Pal type (0;1) interpolation problem on the unit circle considering two disjoint sets of nodes. The nodal points are obtained by projecting vertically the zeros of the Jacobi polynomial P _n^{(α,β)}(x) and its derivative P _n^{(α,β)'}(x) , together with ±1 onto the unit circle. The Lagrange data are prescribed...
Article
Full-text available
This research article aims to staunchly study the approximation using Lagrange interpolation on the unit circle. Nodal system constitutes the vertically projected zeros of Jacobi polynomial onto the unit circle with boundary points at ±1. Moreover, convergence is obtained by considering analytic functions on a suitable domain accompanied by some nu...
Preprint
Full-text available
The paper is devoted to the study of a Pál type (0; 1) interpolation problem on the unit circle considering two disjoint sets of nodes. The nodal points are obtained by projecting vertically the zeros of the Jacobi polynomial P_n^(α, β)(x) and its derivative P_n^(α, β)' (x), together with ±1 onto the unit circle. The Lagrange data are prescribed on...
Preprint
Full-text available
The aim of this paper is to study the approximation of functions using a higher order Hermite-Fejer interpolation process on the unit circle. The system of nodes is composed of vertically projected zeros of Jacobi polynomials onto the unit circle with boundary points at $ \pm1 $. Values of the polynomial and its first four derivatives are fixed by...
Article
Full-text available
In this paper we have constructed a non-interpolatory spline on the unit circle. The rate of convergence and the error in approximation corresponding to the complex valued function has been considered.
Presentation
Full-text available
In this presentation, authors brought into consideration the set of non-uniformly distributed nodes on the unit circle to investigate a Pal-type (1;0) interpolation problem in account with Hermite-Fej´er boundary condition. These nodes are obtained by projecting vertically the zeros of Jacobi polynomial as well as zeros of its derivative onto the u...
Article
Full-text available
In this research manuscript, authors brought into consideration the set of non-uniformly distributed nodes on the unit circle to investigate a Pál-type (1;0) interpolation problem in account with Hermite-Fejér boundary condition. These nodes are obtained by projecting vertically the zeros of Jacobi polynomial as well as zeros of its derivative onto...
Article
Full-text available
This paper deals with the Hermite-Fej´er interpolation problem on the unit circle with the nodal system containing the vertically projected zeros of Jacobi’s polynomial with boundary points on the unit circle. We worked upon three nodal structures throughout this paper and obtained rate of convergence for each case. Moreover, we did a comparison of...
Preprint
This paper deals with the Hermite-Fejér interpolation problem on the unit circle with the nodal system containing the vertically projected zeros of Jacobi's polynomial with boundary points on the unit circle. We worked upon three nodal structures throughout this paper and obtained rate of convergence for each case. Moreover, we did a comparison of...
Preprint
In this research manuscript, authors brought into consideration the set of non-uniformly distributed nodes on the unit circle to investigate a Pal-type (1;0) interpolation problem in account with Hermite-Fejer boundary condition. These nodes are obtained by projecting vertically the zeros of Jacobi polynomial as well as zeros of its derivative onto...
Preprint
In this paper we have constructed a non-interpolatory spline on the unit circle. The rate of convergence and the error in approximation corresponding to the complex valued function has been considered.
Presentation
Full-text available
A presentation to get the basic idea of field of Cryptology.
Presentation
Full-text available
The aim of this paper is to study an interpolation problem ,which is an intermediate problem between Lagrange and Hermite. We consider this problem on the nodes obtained by projecting vertically the zeroes of the (1-x^2 )P_n (x) onto the unit circle, where P_n (x) stands for n^th Legendre polynomial. We prove the regularity of the problem, give exp...
Article
Full-text available
The aim of this paper is to study an interpolation problem ,which is an intermediate problem between Lagrange and Hermite. We consider this problem on the nodes obtained by projecting vertically the zeroes of the (1-x^2 )P_n (x) onto the unit circle, where P_n (x) stands for n^th Legendre polynomial. We prove the regularity of the problem, give exp...
Article
Full-text available
The aim of this paper is to study a Lagrange-Hermite interpolation on the nodes, which are obtained by projecting vertically the zeroes of the (1-x^2 )P_n (x) on the unit circle, where P_n (x) stands for n^th Legendre polynomial. We prove the regularity of the problem, give explicit forms and establish a convergence theorem for the same.

Questions

Questions (5)
Question
I wanted to know who went out of box and thought of choosing the interpolation nodes other than the real interval. Also, please attach the research article in this context.
Question
I am aware of the facts that every totally bounded metric space is separable and a metric space is compact iff it is totally bounded and complete but I wanted to know, is every totally bounded metric space is locally compact or not. If not, then give an example of a metric space that is totally bounded but not locally compact.
Follow this question on the given link
Question
It is cited in various research papers as
Fejér, L.: Über Interpolation. Gött. Nachr, 66–91 (1916).
Question
Creating interpolating polynomial on the unit circle by projecting the zeros of certain polynomials vertically on the unit circle as well as reading their convergence behaviour for the functions analytic inside the unit circle can how be seen for the application part in the real life.
Where such type of interpolation can be applied to view a much wider perspective to such type of research problems.
Question
Approximation theory of interpolation is of foundational importance in numerical analysis especially for various scientific computing problems.
Considerable amount of literature got accumulated on Lagrange, Hermite, Lacunary and Pal-type interpolation in past few years. Working out the interpolation on the real line has seen a numerical justification by many researchers, but on the complex plane, particularly I would say the unit disk hasn't seen much of the justification done numerically by the use of different programming platforms.
I would request other researchers who are part of this discussion to help me find out some useful papers in such direction.
I am also currently working through programming platform MATHEMATICA to view out numerical aspects of my research works.
Hope to see you guys with some good results in future discussion.

Network

Cited By

Projects