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.
``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.
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
``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.
``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.
``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/