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Bahman Kalantari
Selected Publications

"A Geometric Modulus Principle for Polynomials"
To appear in The American Mathematical Monthly, December 2011.

"A combinatorial construction of high order algorithms for Finding polynomial roots of known multiplicity"
Proceedings of American Mathematical Society, Volume 18, Number 6, 2010, 1897-1906. With Yi Jin.

"Polynomiography"
To appear in Encylopedia of Creative Computer Graphics (in Japanese). With Ryuji Takaki, 2011.

"Mollified Zone Diagrams and Their Applications"
To appear in Springer’s LNCS Transactions on Computational Science, April 2011. With Sergio de Biasi and Iraj Kalantari

"Polynomial Root-Finding Methods Whose Basins of Attraction Approximate Voronoi Diagram"
Discrete & Computational Geometry, 2011, Volume 46, Number 1, Pages 187-203.

"Maximal Zone Diagrams and Their Applications"
In Proceedings of the Seventh annual International Symposium on Voronoi Diagrams in Science and Engineering, 171-180, June 2010, Quebec City, Canada. With Sergio de Biasi and Iraj Kalantari
http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5521422

"Solving for the Unknown: Forundation for Math and Art"
In Bulletin of the Society for Science on Form, Tokyo, Japan, June 2010, Page 61.

"Permutation Matrices and Polynomiography"
In Symmetry: Art and Science, Special Issues for Festival-Congress, 130-133, August. 2010.

"Polynomial Root-Finding and Polynomiography"
World Scientific, Spring, 2009.
http://www.worldscibooks.com/mathematics/6265.html

"Fundamental theorem of algebra, a fundamental family of iteration functions, and polynomiography"
Appeared in Mathematical Intelligencer, B. Kalantari.

"Polynomiography: a medium for art, math, and education"
Mathematics & Design, Proceedings of Fifth International Conference Mathematics & Design, 63 - 70, 2007. B. Kalantari.

"On general convergence of the Basic Family for extracting radicals"
Journal of Computational and Applied Mathematics, 206, 832-842, 2007. Yi Jin and Bahman Kalantari.

"A procedure of Chvatal's for testing feasibility in linear programming and matrix scaling"
Linear Algebra and its Applications, 416, 2006, 795-798, Yi Jin and Bahman Kalantari.

"On the complexity of general matrix scaling and entropy minimization via the RAS algorithm"
Mathematical Programming, Series A, 112, 371-401. B. Kalantari, I. Lari, F. Ricca, B. Simeone.

"Symmetric functions and root-finding algorithms"
Advances in Applied Mathematics, 34, 2005, 156-174, Y. Jin and B. Kalantari.

"Polynomiography: From the Fundamental Theorem of Algebra to Art"
LEONARDO, Vol. 38, No. 3, 233-238, 2005, B. Kalantari.

"Two and Three-Dimensional Art Inspired by Polynomiography"
Proceedings of Bridges (Mathematical Connections in Art, Music, and Science), Canada, 321-328, 2005. Also, Visual Mathematics, Volume 8, No 1, 2006, B. Kalantari.

"Measuring the average performance of root-finding algorithms and imaging it through polynomiography"
Proceedings of 17th IMACS World Congress, Scientific Computation, Applied Mathematics and Simulation Paris, France, 2005, F. Andreev, B. Kalantari, I. Kalantari.

"An algebraic derivation of a variant of Basic Family for finding multiple roots of a polynomial"
Proceedings of 17th IMACS World Congress, Scientific Computation, Applied Mathematics and Simulation Paris, France, 2005, Y. Jin and B. Kalantari.

"Animation of mathematical concepts using polynomiography"
Proceedings of SIGGRAPH 2004 on Education, B. Kalantari, I. Kalantari, F. Andreev.

"On homogeneous linear recurrence relations and approximation of zeros of complex polynomials"
DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Unusual Applications in Number Theory, Volume 64, 2004, 125-143, B. Kalantari.

"An infinite family of bounds on zeros of analytic functions and relationship to Smale's bound"
Mathematics of Computation, Volume 74, Number 250, 841-852, 2004, B. Kalantari.

"Polynomiography and application in art, education, and science"
Computers & Graphics, 28, 2004, 417-430, B. Kalantari.

"A new medium for visual art: Polynomiography"
Computer Graphics Quarterly, 38, August 2004, 22-24, B. Kalantari.

"Polynomiography in art and design"
Mathematics & Design, Vol. 4, 2004, 305-311. Proceedings of Fourth International Conference Mathematics & Design, B. Kalantari.

"On the extraneous fixed-points of the basic family of iteration functions"
BIT, 43, 2003, 453-458, B. Kalantari and Y. Jin.

"Semidefinite programming and matrix scaling over the semidefinite cone"
Linear Algebra and its Applications, 375, 2003, 221-243, B. Kalantari.

"Polynomiography and Applications in Art, Education, and Science"
In Proceedings of SIGGRAPH 2003 on Education, B. Kalantari.

"The Art in Polynomiography of Special Polynomials"
In Proceedings of ISAMA/BRIDGES Conference, 173-180, 2003, B. Kalantari..

"Can Polynomiography be Useful in Computational Geometry?"
DIMACS Workshop on Computational Geometry, New Brunswick, NJ, November, 2002, B. Kalantari.
http://dimacs.rutgers.edu/Workshops/CompGeom/abstracts/005.pdf

"Polynomiography: New Visions in Mathematics and Art"
DCIS EXPLORER, Newsletter of the DCIS, Rutgers, Volume 1, Issue 1, 3-7, Fall 2001. B. Kalantari.

"A Determinantal lower bound"
Linear Algebra and its Applications, 326, 2001, 151-159, B. Kalantari and T. H. Pate.

"A computational comparison of the first nine members of a determinantal family of root-finding methods"
Journal of Computational and Applied Math., 130, 2001, 197-204, B. Kalantari and S. Park.

"Generalization of Taylor's theorem and Newton's method via a new family of determinantal interpolation formulas"
Journal of Computational and Applied Mathematics, 126, 2000, 287-318, B. Kalantari.

"New formulas for approximation of Pi and other transcendental numbers"
Numerical Algorithms, 24, 2000, 59-81, B. Kalantari.

"Newton's method and the generation of a determinantal family of iteration functions"
Journal of Computational and Applied Mathematics, 116, 2000, 195-200, B. Kalantari and J. Gerlach.

"A general class of heuristics for minimum weight perfect matching and fast special cases with doubly and triply logarithmic errors"
Algorithmica, 18, 1997, 544-559, C. Imielinska and B. Kalantari.

"On the complexity of matrix balancing"
SIAM Journal on Matrix Analysis, 18, 1997, 450-463, B. Kalantari, L. Khachiyan, and A. Shokoufandeh.

"On linear programming and matrix scaling over the algebraic numbers"
Linear Algebra and its Applications, 262, 1997, 283-306, B. Kalantari and M.R. Emamy-K.

"A basic family of iteration functions for polynomial root finding and its characterizations"
Journal of Computational and Applied Mathematics, 80, 1997, 209-226, B. Kalantari, I. Kalantari, and R. Zaare-Nahandi.

"A Theorem of the alternative for multihomogeneous functions and its relationship to diagonal scaling of matrices"
Linear Algebra and its Application, 236, 1996, 1-24, B. Kalantari.

"On the complexity of nonnegative matrix scaling"
Linear Algebra and its Application, 240, 1996, 87-103, B. Kalantari and L. Khachiyan.

"High order iterative methods for approximating square roots"
BIT, 36, 1996, 395-399, B. Kalantari and I. Kalantari.

"On the order of convergence of a determinantal family of root-finding methods"
BIT, 39, 1996, 395-399. B. Kalantari.

"A simple polynomial time algorithm for a convex hull problem equivalent to linear programming"
Combinatorics Advances, Kluwer Academic Publishers, 1995, 207-216, B. Kalantari.

"Sharp bounds for the maximum of chi-square index in a class of contingency tables with given marginals"
Computational Statistics and Data Analysis}, 16, 1993, 19-34, B. Kalantari, I. Lari, A. Rizzi, and B. Simeone.

"A greedy heuristics for a minimum-weight forest problem"
Operation Research Letters, 14, 1993, 65-71, C. Imielinska, B. Kalantari, and L. Khachiyan.

"On the rate of convergence of deterministic and randomized RAS matrix scaling algorithm," Operations Research Letters"
14, 1993, 237-244, B. Kalantari and L.Khachiyan.

"Generalization of Karmarkar's algorithm to convex homogeneous functions"
Operation Research Letters, 11, 1992, 93-98, B. Kalantari.

"Diagonal matrix scaling and linear programming"
SIAM Journal on Optimization, 4, 1992, 668-672, L. Khachiyan and B. Kalantari.

"A generalized hypergreedy algorithm for perfect matching"
BIT, 33, 1991, 178-189, C. Imielinska and B. Kalantari.

"Canonical problems for quadratic programming and Projective Methods for their Solution"
Contemporary Mathematics, 114 , 1990, 243-263, B. Kalantari.

"Karmarkar's algorithm with improved steps"
Mathematical Programming, 46, 1990, 73-78, B. Kalantari.

"An algorithm for quadratic zero-one program"
Naval Research Logistics Quarterly, 37, 1990, 527-538, B. Kalantari and A. Bagchi.

"Approximating the diameter of a set of points in the Euclidean space"
Information Processing Letters, 32, 1989, 205-211, O. Egecioglu and B. Kalantari.

"A new class of heuristic algorithms for weighted perfect matching"
Journal of the Association for Computing Machinery, Vol. 35, No. 4, 1988, 769-776, M.D. Grigoriadis and B. Kalantari.

"Penalty formulation for zero-one nonlinear programming"
Discrete Applied Mathematics, 16, 1987, 179-182, B. Kalantari and J.B. Rosen.

"An algorithm for global minimization of linearly constrained concave quadratic function"
Mathematics of Operations Research, 12, 1987, 544-561, B. Kalantari and J.B. Rosen.

"A bound on roof-duality gap"
Lecture Notes in Mathematics, Combinatorial Optimization, Como 1986, 254-257, P. L. Hammer and B. Kalantari.

"Quadratic functions with an exponential number of local maxima"
Operations Research Letters, 5, 1986, 47-49, B. Kalantari.

"Construction of large scale global minimum concave quadratic test problems"
Journal of Optimization Theory and Applications, 48, 1986, 303-313, B. Kalantari and J.B. Rosen.

"Construction of difficult linearly constrained concave minimization problems"
Operations Research, 33, 1985, 222-227, B. Kalantari.

"An algorithm for the traveling salesman problem with pickup and delivery customers"
European Journal of Operations Research, 22, 1985, 377-386, B. Kalantari, A.V. Hill and S.R. Arora.

"Penalty for zero-one equivalent problem"
Mathematical Programming, 24, 1982, 229-232, B. Kalantari and J.B. Rosen.

Technical Reports

"Matrix Scaling Dualities in Convex Programming"
2005. Bahman Kalantari
http://www.cs.rutgers.edu/~kalantar/convex2005.pdf

"Some Algebraic-Geometric Properties of Polynomials and Strong Gauss-Lucas and Maximum Modulus Theorems"
Technical Report, 2007, B. Kalantari.

"A Combinatorial Construction of High Order Algorithms for Finding Polynomial Roots of Known Multiplicity"
Y. Jin and B. Kalantari.

Mathermatical Poems

"Zumber"
(A methamtical notion that combined sets and numbets) B. Kalantari.
http://www.cs.rutgers.edu/~kalantar/zumberpoem.pdf

"Heaven's Lakes and Waterfalls"
forthcoming (A coneptualization of the dynamics of iretaions of rational functions) (see Polynomial Root-Finding and Polynomiography --- also a related animation, "Rise of Polynomials" on YouTube)


Copyright © 2011 Bahman Kalantari All Rights Reserved Polynomiography™