245 citations · 253 across the 7 of their papers we have counts for
8 papers
Complexity Analysis of Root Clustering for a Complex Polynomial
Ruben Becker, Michael Sagraloff, Vikram Sharma +2
Let be an arbitrary complex polynomial. We introduce the local root clustering problem, to compute a set of natural -clusters of roots of in some box reg…
Isotopic Arrangement of Simple Curves: an Exact Numerical Approach based on Subdivision
Jyh-Ming Lien, Vikram Sharma, Gert Vegter +1
This paper presents the first purely numerical (i.e., non-algebraic) subdivision algorithm for the isotopic approximation of a simple arrangement of curves. The arrangement is "sim…
Generalizing The Davenport-Mahler-Mignotte Bound -- The Weighted Case
Vikram Sharma
Root separation bounds play an important role as a complexity measure in understanding the behaviour of various algorithms in computational algebra, e.g., root isolation algorithms…
Complexity of a Root Clustering Algorithm
Prashant Batra, Vikram Sharma
Approximating the roots of a holomorphic function in an input box is a fundamental problem in many domains. Most algorithms in the literature for solving this problem are condition…
Bounds on Distance to Variety in Terms of Coefficients of Bivariate Polynomials
Vikram Sharma
A short note on bounds on distance to variety of a point in terms of the Taylor coefficients at the point.
A Near-Optimal Subdivision Algorithm for Complex Root Isolation based on the Pellet Test and Newton Iteration
Ruben Becker, Michael Sagraloff, Vikram Sharma +1
We describe a subdivision algorithm for isolating the complex roots of a polynomial . Given an oracle that provides approximations of each of the coefficients of…
Near Optimal Subdivision Algorithms for Real Root Isolation
Vikram Sharma, Prashant Batra
We describe a subroutine that improves the running time of any subdivision algorithm for real root isolation. The subroutine first detects clusters of roots using a result of Ostro…
No-Switching Quantum Key Distribution using Broadband Modulated Coherent Light
Andrew M. Lance, Thomas Symul, Vikram Sharma +3
We realize an end-to-end no-switching quantum key distribution protocol using continuous-wave coherent light. We encode weak broadband Gaussian modulations onto the amplitude and p…