Polynomiography

Publications

Selected Publications 


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


``Fundamental theorem of algebra, a  fundamental family of iteration functions, and polynomiography," To appear 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. Available at:
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.

MATHEMATICAL 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) http://www.youtube.com/watch?v=kMP0vclKlDA&eurl=http://www.polynomiography.com/