Zobrazeno 1 - 10
of 176
pro vyhledávání: '"Kalantari, Bahman"'
Autor:
Lau, Chun, Kalantari, Bahman
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 Kalantari \cite{kalantari23}. The algorithms compute an approximate so
Externí odkaz:
http://arxiv.org/abs/2304.12168
Autor:
Kalantari, Bahman
We develop novel theory and algorithms for computing approximate solution to $Ax=b$, or to $A^TAx=A^Tb$, where $A$ is an $m \times n$ real matrix of arbitrary rank. First, we describe the {\it Triangle Algorithm} (TA), where given an ellipsoid $E_{A,
Externí odkaz:
http://arxiv.org/abs/2304.04940
Autor:
Kalantari, Bahman
Building on a classification of zeros of cubic equations due to the $12$-th century Persian mathematician Sharaf al-Din Tusi, together with Smale's theory of {\it point estimation}, we derive an efficient recipe for computing high-precision approxima
Externí odkaz:
http://arxiv.org/abs/2303.17747
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 mathematical historian Rashed, Tusi analyzed the problem for five differe
Externí odkaz:
http://arxiv.org/abs/2201.13282
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 linear system $Ax=b$, where $A$ is an $m \times n$ matrix of arbitrary ran
Externí odkaz:
http://arxiv.org/abs/2004.12978
Autor:
Kalantari, Bahman
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 exhibit chaotic behavior and is only guaranteed to converge locally. Bas
Externí odkaz:
http://arxiv.org/abs/2003.00372
Autor:
Hohertz, Matt, Kalantari, Bahman
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 number, multiply by three and add one if the number is odd, halve the
Externí odkaz:
http://arxiv.org/abs/2001.00482
On the Equivalence of SDP Feasibility and a Convex Hull Relaxation for System of Quadratic Equations
Autor:
Kalantari, Bahman
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 one hand, this offers a simple description of SDP. On the other hand, th
Externí odkaz:
http://arxiv.org/abs/1911.03989
Autor:
Kalantari, Bahman
Given $n \times n$ real symmetric matrices $A_1, \dots, A_m$, the following {\it spectral minimax} property holds: $$\min_{X \in \mathbf{\Delta}_n} \max_{y \in S_m} \sum_{i=1}^m y_iA_i \bullet X=\max_{y \in S_m} \min_{X \in \mathbf{\Delta}_n} \sum_{i
Externí odkaz:
http://arxiv.org/abs/1905.09762