5 citations · 34 across the 24 of their papers we have counts for
7 papers · 1 filter
An Algorithmic Separating Hyperplane Theorem and Its Applications
Bahman Kalantari
We first prove a new separating hyperplane theorem characterizing when a pair of compact convex subsets of the Euclidean space intersect, and when they are disjoint. The th…
Randomized Triangle Algorithms for Convex Hull Membership
Bahman Kalantari
We present randomized versions of the {\it triangle algorithm} introduced in \cite{kal14}. The triangle algorithm tests membership of a distinguished point in…
Newton-Ellipsoid Method and its Polynomiography
Bahman Kalantari, Eric Lee
We introduce a new iterative root-finding method for complex polynomials, dubbed {\it Newton-Ellipsoid} method. It is inspired by the Ellipsoid method, a classical method in optimi…
Fast Approximation and Randomized Algorithms for Diameter
Sharareh Alipour, Bahman Kalantari, Hamid Homapour
We consider approximation of diameter of a set of points in dimension . Eeciolu and Kalantari \cite{kal} have shown that given any , by co…
A One-Line Proof of the Fundamental Theorem of Algebra with Newton's Method as a Consequence
Bahman Kalantari
Many proofs of the fundamental theorem of algebra rely on the fact that the minimum of the modulus of a complex polynomial over the complex plane is attained at some complex number…
Algorithms and Polynomiography for Solving Quaternion Quadratic Equations
Fedor Andreev, Bahman Kalantari
Solving a quadratic equation with real coefficients is known to middle school students. Solving the equation over the quaternions is not straightforward. Huang a…
Solving Cubic Equations By the Quadratic Formula
Bahman Kalantari
Let be a monic cubic complex polynomial with distinct roots and distinct critical points. We say a critical point has the {\it Voronoi property} if it lies in the Voronoi ce…