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)*