5 citations · 34 across the 24 of their papers we have counts for
29 papers
Spherical Convex Hull Membership: Complexity and Performance of Geometric and Accelerated Methods
Bahman Kalantari
We study the problem of testing membership of the origin in the convex hull of unit vectors in , seeking a convex combination of norm at most or a s…
On the Performance of a Novel Class of Linear System Solvers and Comparison with State-of-The-Art Algorithms
Chun Lau, Bahman Kalantari
We present a comprehensive computational study of a class of linear system solvers, called {\it Triangle Algorithm} (TA) and {\it Centering Triangle Algorithm} (CTA), developed by…
A Family of Iteration Functions for General Linear Systems
Bahman Kalantari
We introduce innovative algorithms for computing exact or approximate (minimum-norm) solutions to or the {\it normal equation} , where is an rea…
Solution of Real Cubic Equations without Cardano's Formula
Bahman Kalantari
Building on a classification of zeros of cubic equations due to the -th century Persian mathematician Sharaf al-Din Tusi, together with Smale's theory of {\it point estimation}…
On Tusi's Classification of Cubic Equations and its Connections to Cardano's Formula and Khayyam's Geometric Solution
Bahman Kalantari, Rahim Zaare-Nahandi
Omar Khayyam's studies on cubic equations inspired the 12th century Persian mathematician Sharaf al-Din Tusi to investigate the number of positive roots. According to the noted mat…
A Geometric Algorithm for Solving Linear Systems
Bahman Kalantari, Chun Lau, Yikai Zhang
Based on the geometric {\it Triangle Algorithm} for testing membership of a point in a convex set, we present a novel iterative algorithm for testing the solvability of a real line…
A Globally Convergent Newton Method for Polynomials
Bahman Kalantari
Newton's method for polynomial root finding is one of mathematics' most well-known algorithms. The method also has its shortcomings: it is undefined at critical points, it could ex…
Collatz polynomials: an introduction with bounds on their zeros
Matt Hohertz, Bahman Kalantari
The Collatz Conjecture (also known as the 3x+1 Problem) proposes that the following algorithm will, after a certain number of iterations, always yield the number 1: given a natural…
On the Equivalence of SDP Feasibility and a Convex Hull Relaxation for System of Quadratic Equations
Bahman Kalantari
We show {\it semidefinite programming} (SDP) feasibility problem is equivalent to solving a {\it convex hull relaxation} (CHR) for a finite system of quadratic equations. On the on…
A Spectral Generalization of Von Neumann Minimax Theorem
Bahman Kalantari
Given real symmetric matrices , the following {\it spectral minimax} property holds: $$\min_{X \in \mathbfΔ_n} \max_{y \in S_m} \sum_{i=1}^m y_iA_i \b…
A Triangle Algorithm for Semidefinite Version of Convex Hull Membership Problem
Bahman Kalantari
Given a subset of , the set of real symmetric matrices, we define its {\it spectrahull} as the set $SH(\mathbf{S}) = \{p…
Spherical Triangle Algorithm: A Fast Oracle for Convex Hull Membership Queries
Bahman Kalantari, Yikai Zhang
The it Convex Hull Membership(CHM) problem is: Given a point and a subset of points in , is ? CHM is not only a fundamental problem in Line…
Approximating Bimatrix Nash Equilibrium Via Trilinear Minimax
Bahman Kalantari
The Bimatrix Nash Equilibrium (NE) for real matrices and , denoted as the {\it Row} and {\it Column} players, is characterized as follows: Let $Δ=S_m \times S_n…
The edge-vertex inequality in a planar graph and a bipartition for the class of all planar graphs
M. R. Emamy-K., Bahman Kalantari, Tatiana Correa
For a planar graph with a given f-vector we introduce a cubic polynomial whose coefficients depend on the f-vector. The planar graph is said to be real if…
Robust Vertex Enumeration for Convex Hulls in High Dimensions
Pranjal Awasthi, Bahman Kalantari, Yikai Zhang
Computation of the vertices of the convex hull of a set of points in is a fundamental problem in computational geometry, optimization, machine learning and…
An Invitation to Polynomiography via Exponential Series
Bahman Kalantari
The subject of Polynomiography deals with algorithmic visualization of polynomial equations, having many applications in STEM and art, see [Kal04]. Here we consider the polynomiogr…
A Comparison of the Triangle Algorithm and SMO for Solving the Hard Margin Problem
Mayank Gupta, Bahman Kalantari
In this article we consider the problem of testing, for two finite sets of points in the Euclidean space, if their convex hulls are disjoint and computing an optimal supporting hyp…
How Many Real Attractive Fixed Points Can A Polynomial Have?
Terence Coelho, Bahman Kalantari
We prove a complex polynomial of degree has at most attractive fixed points lying on a line. We also consider the general case.
A Necessary and Sufficient Condition for Local Maxima of Polynomial Modulus Over Unit Disc
Bahman Kalantari
An important quantity associated with a complex polynomial is , the maximum of its modulus over the unit disc . We prove, is a local max…
On intersective polynomials with non-solvable Galois group
Joachim König
We present new theoretical results on the existence of intersective polynomials with certain prescribed Galois groups, namely the projective and affine linear groups …
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…