5 citations · 34 across the 24 of their papers we have counts for
12 papers · 1 filter
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}…
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…
The Robust Newton Method for Polynomials and its Polynomiography
Bahman Kalantari
We present the Robust Newton Method (RNM) for a complex polynomial of degree , with continuous map , where $A(z)=\max_{0\leq j\le…
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…
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…
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…
Solving Linear System of Equations Via A Convex Hull Algorithm
Bahman Kalantari
We present new iterative algorithms for solving a square linear system in dimension by employing the {\it Triangle Algorithm} \cite{kal12}, a fully polynomial-time appro…