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- BAHMAN KALANTARI
- 1998

In this paper first we prove four fundamental theorems of the alternative, called scaling dualities, characterizing exact and approximate solvability of four significant conic problems in finite dimensional spaces, defined as: homogeneous programming (HP), scaling problem (SP), homogeneous scaling problem (HSP), and algebraic scaling problem (ASP). Let φ be… (More)

We consider convex programming problems in a canonical homogeneous format, a very general form of Karmarkar's canonical linear programming problem. More specifically, by homogeneous programming we shall refer to the problem of testing if a homogeneous convex function has a nontrivial zero over a subspace and its intersection with a pointed convex cone. To… (More)

- Bahman Kalantari
- 2008

Kalantari This book offers fascinating and modern perspectives into the theory and practice of the historical subject of polynomial root-finding, rejuvenating the field via polynomiography, a creative and novel computer visualization that renders spectacular images of a polynomial equation. Polynomiography will not only pave the way for new applications of… (More)

Given a set P with n points in R li, its diameter d, is the maximum of the Euclidean distances between its points. We describe an algorithm that in m < n iterations obtains r, < rs <. .). For k fixed, the cost of each iteration is O(n). In particular, the first approximation r, is within fi of dp, independent of the dimension k.

Let p(x) be a polynomial of degree n 2 with coecients in a subeld K of the complex numbers. For each natural number m 2, let L m (x) be the m 2 m lower triangular matrix whose diagonal entries are p(x) and for each j = 1; : : : ; m 0 1, its j-th subdiagonal entries are p (j) (x)=j!. For i = 1; 2, let L (i) m (x) be the matrix obtained from L m (x) by… (More)

- Bahman Kalantari
- 1997

The general form of Taylor's theorem gives the formula, f = P n + R n , where P n is the New-ton's interpolating polynomial, computed with respect to a connuent vector of nodes, and R n is the remainder. When f 0 6 = 0, for each m = 2; : : :; n + 1, we describe a \determinantal interpolation formula", f = P m;n +R m;n , where P m;n is a rational function in… (More)