• 611 Citations
  • 16 h-Index
1982 …2019
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Research Output 1982 2019

2019
1 Citation (Scopus)

An algorithmic separating hyperplane theorem and its applications

Kalantari, B., Mar 15 2019, In : Discrete Applied Mathematics. 256, p. 59-82 24 p.

Research output: Contribution to journalArticle

Hyperplane
Iteration
Triangle
Theorem
Pivot

Newton–Ellipsoid polynomiography

Kalantari, B. & Lee, E. H., Jan 1 2019, In : Journal of Mathematics and the Arts.

Research output: Contribution to journalArticle

Newton-Raphson method
Newton Methods
Ellipsoid Method
Polynomial equation
Iterative methods
2018
2 Citations (Scopus)

Robust vertex enumeration for convex hulls in high dimensions

Awasthi, P., Kalantari, B. & Zhang, Y., Jan 1 2018, p. 1387-1396. 10 p.

Research output: Contribution to conferencePaper

Vertex Enumeration
Convex Hull
Higher Dimensions
Non-negative Matrix Factorization
Vertex of a graph
2014
4 Citations (Scopus)

A characterization theorem and an algorithm for a convex hull problem

Kalantari, B., Jan 1 2014, In : Annals of Operations Research. 226, 1, p. 301-349 49 p.

Research output: Contribution to journalArticle

Convex hull
Duality
Factors
Visibility
Simplex method
2013
16 Citations (Scopus)

Algorithms for quaternion polynomial root-finding

Kalantari, B., Jan 1 2013, In : Journal of Complexity. 29, 3-4, p. 302-322 21 p.

Research output: Contribution to journalArticle

Polynomial Roots
Root-finding
Quaternion
Polynomials
Algebra
1 Citation (Scopus)

On properties of forbidden zones of polygons and polytopes

Berkowitz, R., Kalantari, B., Kalantari, I. & Menendez, D., Dec 1 2013, Transactions on Computational Science XX: Special Issue on Voronoi Diagrams and Their Applications. p. 112-137 26 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 8110).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Polytopes
Polygon
Circumference
Diagram
Voronoi Diagram

The state of the art of voronoi diagram research

Kalantari, B., Dec 1 2013, Transactions on Computational Science XX: Special Issue on Voronoi Diagrams and Their Applications. p. 1-4 4 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 8110).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Voronoi Diagram
2012
2 Citations (Scopus)

Finding a lost treasure in convex hull of points from known distances

Kalantari, B., Dec 1 2012, p. 271-276. 6 p.

Research output: Contribution to conferencePaper

Convex Hull
Ambiguous
Euclidean Distance
Decision problem
Set of points
2 Citations (Scopus)

On properties of forbidden zones of polygons and polytopes

Berkowitz, R., Kalantari, B., Menendez, D. & Kalantari, I., Oct 3 2012, Proceedings of the 2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012. p. 56-65 10 p. 6257657. (Proceedings of the 2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Polytopes
Polygon
Circumference
Circle
Ball
2 Citations (Scopus)

Voronoi diagram properties in polynomials with polynomiography applications and extensions

Kalantari, B., Oct 3 2012, Proceedings of the 2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012. p. 32-40 9 p. 6257654

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Voronoi Diagram
Polynomial
Basin of Attraction
Roots of a cubic
Visualization
2011
4 Citations (Scopus)

Alternating sign matrices and polynomiography

Kalantari, B., Nov 10 2011, In : Electronic Journal of Combinatorics. 18, 2, p. 1-22 22 p.

Research output: Contribution to journalArticle

Alternating Sign Matrices
Polytopes
Polynomials
Polynomial
Iteration Function
8 Citations (Scopus)

Mollified zone diagrams and their computation

De Biasi, S. C., Kalantari, B. & Kalantari, I., Nov 25 2011, Transactions on Computational Science XIV - Special Issue on Voronoi Diagrams and Delaunay Triangulation. p. 31-59 29 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 6970 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Diagram
Zorn's lemma
Euclidean plane
Fixed Point Theory
Voronoi Diagram
12 Citations (Scopus)

Polynomial Root-Finding Methods Whose Basins of Attraction Approximate Voronoi Diagram

Kalantari, B., Jul 1 2011, In : Discrete and Computational Geometry. 46, 1, p. 187-203 17 p.

Research output: Contribution to journalArticle

Polynomial Roots
Root-finding
Basin of Attraction
Voronoi Diagram
Rational functions
2010
1 Citation (Scopus)
Polynomial Roots
Iteration Function
Multiplicity
Polynomials
Higher Order
6 Citations (Scopus)

Maximal zone diagrams and their computation

De Biasi, S. C., Kalantari, B. & Kalantari, I., Aug 23 2010, ISVD 2010 - 7th International Symposium on Voronoi Diagrams in Science and Engineering. p. 171-180 10 p. 5521422

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Diagram
Zorn's lemma
Euclidean plane
Fixed Point Theory
Voronoi Diagram
2009
8 Citations (Scopus)

Voronoi diagrams and polynomial root-finding

Kalantari, B., Dec 1 2009, 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009. p. 31-40 10 p. 5362425. (6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Polynomial Roots
Root-finding
Voronoi Diagram
Voronoi Cell
Polynomials
2008
20 Citations (Scopus)

On the complexity of general matrix scaling and entropy minimization via the RAS algorithm

Kalantari, B., Lari, I., Ricca, F. & Simeone, B., Apr 1 2008, In : Mathematical Programming. 112, 2, p. 371-401 31 p.

Research output: Contribution to journalArticle

Entropy
Scaling
Nonnegative Matrices
Polynomials
Square matrix
52 Citations (Scopus)

Polynomial root-finding and polynomiography

Kalantari, B., Jan 1 2008, World Scientific Publishing Co. 467 p.

Research output: Book/ReportBook

Polynomial Roots
Root-finding
Visualization
Linear Recurrence Relation
Iteration Function
2007
2 Citations (Scopus)

On general convergence in extracting radicals via a fundamental family of iteration functions

Jin, Y. & Kalantari, B., Sep 15 2007, In : Journal of Computational and Applied Mathematics. 206, 2, p. 832-842 11 p.

Research output: Contribution to journalArticle

Iteration Function
Newton-Raphson method
Algebra
Visualization
Newton Methods
2006
7 Citations (Scopus)

A procedure of Chvátal for testing feasibility in linear programming and matrix scaling

Jin, Y. & Kalantari, B., Jul 15 2006, In : Linear Algebra and Its Applications. 416, 2-3, p. 795-798 4 p.

Research output: Contribution to journalArticle

Linear programming
Scaling
Testing
Diagonal matrix
Linear systems
2005
18 Citations (Scopus)

An infinite family of bounds on zeros of analytic functions and relationship to smale's bound

Kalantari, B., Apr 1 2005, In : Mathematics of Computation. 74, 250, p. 841-852 12 p.

Research output: Contribution to journalArticle

Analytic function
Complex Polynomials
Polynomials
Lower bound
Iteration Function
1 Citation (Scopus)
Analytic function
Zero
Family
Relationships
23 Citations (Scopus)

Polynomiography: From the fundamental theorem of Algebra to art

Kalantari, B., Jan 1 2005, In : Leonardo. 38, 3, p. 233-238 6 p.

Research output: Contribution to journalArticle

Algebra
Polynomials
Coloring
Masks
Visualization
5 Citations (Scopus)

Symmetric functions and root-finding algorithms

Jin, Y. & Kalantari, B., Jan 1 2005, In : Advances in Applied Mathematics. 34, 1, p. 156-174 19 p.

Research output: Contribution to journalArticle

Root-finding
Symmetric Functions
Iteration Function
Derivatives
Multiple Roots
2004
4 Citations (Scopus)

Animation of mathematical concepts using polynomiography

Kalantari, B., Kalantari, I. & Andreev, F., Dec 1 2004, ACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04. 1 p. (ACM SIGGRAPH 2004: Educators Program, SIGGRAPH'04).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Animation
visualization
Polynomials
Visualization
art
24 Citations (Scopus)

Polynomiography and applications in art, education, and science

Kalantari, B., Jun 1 2004, In : Computers and Graphics (Pergamon). 28, 3, p. 417-430 14 p.

Research output: Contribution to journalArticle

Education
Polynomials
Fractals
Algebra
Geometry
2003
3 Citations (Scopus)

Semidefinite programming and matrix scaling over the semidefinite cone

Kalantari, B., Dec 1 2003, In : Linear Algebra and Its Applications. 375, 1-3, p. 221-243 23 p.

Research output: Contribution to journalArticle

Semidefinite Programming
Solvability
Cones
Cone
Scaling
2001
8 Citations (Scopus)
Root-finding
Polynomials
Order of Convergence
Newton-Raphson method
Natural number
5 Citations (Scopus)

A determinantal lower bound

Kalantari, B. & Pate, T. H., Mar 15 2001, In : Linear Algebra and Its Applications. 326, 1-3, p. 151-159 9 p.

Research output: Contribution to journalArticle

Lower bound
Modulus
Circle theorem
Polynomials
Trace Inequality
2000
28 Citations (Scopus)
Taylor's theorem
Newton-Raphson method
Newton Methods
Interpolation
Interpolate
4 Citations (Scopus)

New formulas for approximation of π and other transcendental numbers

Kalantari, B., Dec 1 2000, In : Numerical Algorithms. 24, 1-2, p. 59-81 23 p.

Research output: Contribution to journalArticle

Transcendental number
Approximation
Taylor's theorem
Iteration Function
Algebraic extension
21 Citations (Scopus)

Newton's method and generation of a determinantal family of iteration functions

Kalantari, B. & Gerlach, J., Apr 1 2000, In : Journal of Computational and Applied Mathematics. 116, 1, p. 195-200 6 p.

Research output: Contribution to journalArticle

Iteration Function
Newton-Raphson method
Newton Methods
Halley's Method
Precise Asymptotics
1999
18 Citations (Scopus)

On the Order of Convergence of a Determinantal Family of Root-Finding Methods

Kalantari, B., Jan 1 1999, In : BIT Numerical Mathematics. 39, 1, p. 96-109 14 p.

Research output: Contribution to journalArticle

Root-finding
Order of Convergence
Natural number
Determinant
Generalized Fibonacci numbers
1997
35 Citations (Scopus)

A basic family of iteration functions for polynomial root finding and its characterizations

Kalantari, B., Kalantari, I. & Zaare-Nahandi, R., May 5 1997, In : Journal of Computational and Applied Mathematics. 80, 2, p. 209-226 18 p.

Research output: Contribution to journalArticle

Iteration Function
Polynomial Roots
Root-finding
Polynomials
Roots

A General Class of Heuristics for Minimum Weight Perfect Matching and Fast Special Cases with Doubly and Triply Logarithmic Errors

Imielińska, C. & Kalantari, B., Jan 1 1997, In : Algorithmica (New York). 18, 4, p. 544-559 16 p.

Research output: Contribution to journalArticle

Perfect Matching
Heuristic algorithms
Logarithmic
Heuristics
Heuristic algorithm
3 Citations (Scopus)

On linear programming and matrix scaling over the algebraic numbers

Kalantari, B. & Emamy-K, M. R., Sep 1 1997, In : Linear Algebra and Its Applications. 262, 1-3, p. 283-306 24 p.

Research output: Contribution to journalArticle

Algebraic number
Linear programming
Scaling
Polynomials
Interior-point Algorithm
17 Citations (Scopus)

On the complexity of matrix balancing

Kalantari, B., Khachiyan, L. & Shokoufandeh, A., Jan 1 1997, In : SIAM Journal on Matrix Analysis and Applications. 18, 2, p. 450-463 14 p.

Research output: Contribution to journalArticle

Balancing
Non-negative
Convex Programming
Diagonal matrix
Sensitivity Analysis
1996
7 Citations (Scopus)
Theorems of the Alternative
Logarithmic Barrier Function
Stationary point
Scaling
Scalability
4 Citations (Scopus)

Magic labeling in graphs: Bounds, complexity, and an application to a variant of TSP

Kalantari, B. & Khosrovshahi, G. B., Jan 1 1996, In : Networks. 28, 4, p. 211-219 9 p.

Research output: Contribution to journalArticle

Labeling
Stars
Labels
Testing
32 Citations (Scopus)

On the complexity of nonnegative-matrix scaling

Kalantari, B. & Khachiyan, L., Jan 1 1996, In : Linear Algebra and Its Applications. 240, p. 87-103 17 p.

Research output: Contribution to journalArticle

Scaling Factor
Nonnegative Matrices
Scaling
Polynomial-time Complexity
Positive Matrices
1993

A generalized hypergreedy algorithm for weighted perfect matching

Imielinska, C. & Kalantari, B., Jun 1 1993, In : BIT. 33, 2, p. 177-189 13 p.

Research output: Contribution to journalArticle

Perfect Matching
Triangle inequality
Euclidean plane
Weighted Graph
Heuristics
23 Citations (Scopus)

A greedy heuristic for a minimum-weight forest problem

Imielińska, C., Kalantari, B. & Khachiyan, L., Jan 1 1993, In : Operations Research Letters. 14, 2, p. 65-71 7 p.

Research output: Contribution to journalArticle

Greedy Heuristics
Approximate Solution
Spanning Forest
Triangle inequality
Minimum Spanning Tree
11 Citations (Scopus)

On the rate of convergence of deterministic and randomized RAS matrix scaling algorithms

Kalantari, B. & Khachiyan, L., Jan 1 1993, In : Operations Research Letters. 14, 5, p. 237-244 8 p.

Research output: Contribution to journalArticle

Rate of Convergence
Scaling
Polynomials
Fully Polynomial Time Approximation Scheme
Positive Matrices
6 Citations (Scopus)

Sharp bounds for the maximum of the chi-square index in a class of contingency tables with given marginals

Kalantari, B., Lari, I., Rizzi, A. & Simeone, B., Jan 1 1993, In : Computational Statistics and Data Analysis. 16, 1, p. 19-34 16 p.

Research output: Contribution to journalArticle

Chi-square
Sharp Bound
Contingency Table
Heuristics
Experiments
1992
1 Citation (Scopus)

Generalization of Karmarkar's algorithm to convex homogeneous functions

Kalantari, B., Jan 1 1992, In : Operations Research Letters. 11, 2, p. 93-98 6 p.

Research output: Contribution to journalArticle

Karmarkar's Algorithm
Homogeneous Function
Convex function
Subspace
Generalization
1990
13 Citations (Scopus)

An algorithm for quadratic zero‐one programs

Kalantari, B. & Bagchi, A., Jan 1 1990, In : Naval Research Logistics (NRL). 37, 4, p. 527-538 12 p.

Research output: Contribution to journalArticle

Quadratic Program
Convex Envelope
Quadratic Function
Conjugate Directions
Feasible region
5 Citations (Scopus)

Karmarkar's algorithm with improved steps

Kalantari, B., Jan 1 1990, In : Mathematical Programming. 46, 1-3, p. 73-78 6 p.

Research output: Contribution to journalArticle

Karmarkar's Algorithm
Linear Program
Feasible region
Dependent Data
Potential Function
1989
16 Citations (Scopus)

Approximating the diameter of a set of points in the Euclidean space

Eg̃eciog̃lu, Ö. & Kalantari, B., Sep 1 1989, In : Information Processing Letters. 32, 4, p. 205-211 7 p.

Research output: Contribution to journalArticle

Diameter of a set
Set of points
Euclidean space
Iteration
Euclidean Distance
1988
6 Citations (Scopus)

A New Class of Heuristic Algorithms for Weighted Perfect Matching

Grigoriadis, M. D. & Kalantari, B., Oct 1 1988, In : Journal of the ACM (JACM). 35, 4, p. 769-776 8 p.

Research output: Contribution to journalArticle

Heuristic algorithms