Kalantari, Bahman
Overview
Works:  40 works in 91 publications in 1 language and 1,973 library holdings 

Roles:  Author, Editor 
Classifications:  QA161.P59, 512.9422 
Publication Timeline
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Most widely held works about
Bahman Kalantari
Most widely held works by
Bahman Kalantari
Polynomial rootfinding and polynomiography by
Bahman Kalantari(
Book
)
17 editions published between 2007 and 2009 in English and Undetermined and held by 110 WorldCat member libraries worldwide
"This book offers fascinating and modern perspectives into the theory and practice of the historical subject of polynomial rootfinding, rejuvenating the field via polynomiography, a creative and novel computer visualization that renders spectacular images of a polynomial equation. Polynomiography will not only pave the way for new applications of polynomials in science and mathematics, but also in art and education. The book presents a thorough development of the basic family, arguably the most fundamental family of iteration functions, deriving many surprising and novel theoretical and practical applications such as: algorithms for approximation of roots of polynomials and analytic functions, polynomiography, bounds on zeros of polynomials, formulas for the approximation of Pi, and characterizations or visualizations associated with a homogeneous linear recurrence relation. These discoveries and a set of beautiful images that provide new visions, even of the wellknown polynomials and recurrences, are the makeup of a very desirable book. This book is a must for mathematicians, scientists, advanced undergraduates and graduates, but is also for anyone with an appreciation for the connections between a fantastically creative art form and its ancient mathematical foundations."Jacket
17 editions published between 2007 and 2009 in English and Undetermined and held by 110 WorldCat member libraries worldwide
"This book offers fascinating and modern perspectives into the theory and practice of the historical subject of polynomial rootfinding, rejuvenating the field via polynomiography, a creative and novel computer visualization that renders spectacular images of a polynomial equation. Polynomiography will not only pave the way for new applications of polynomials in science and mathematics, but also in art and education. The book presents a thorough development of the basic family, arguably the most fundamental family of iteration functions, deriving many surprising and novel theoretical and practical applications such as: algorithms for approximation of roots of polynomials and analytic functions, polynomiography, bounds on zeros of polynomials, formulas for the approximation of Pi, and characterizations or visualizations associated with a homogeneous linear recurrence relation. These discoveries and a set of beautiful images that provide new visions, even of the wellknown polynomials and recurrences, are the makeup of a very desirable book. This book is a must for mathematicians, scientists, advanced undergraduates and graduates, but is also for anyone with an appreciation for the connections between a fantastically creative art form and its ancient mathematical foundations."Jacket
A theorem of the alternative for multihomogeneous functions and its relationship to diagonal scaling of matrices by
Bahman Kalantari(
Book
)
4 editions published between 1989 and 1993 in English and held by 10 WorldCat member libraries worldwide
We prove that either [phi] has a nonnegative zero x in W each of whose component vectors x[superscript (j)] [epsilon] W[subscript j], is nontrivial, or, given an admissible [lambda], the logarithmic barrier function [formula], has a positive constrained stationary point in W, and if [phi] is convex, precisely one of these conditions is satisfied. Moreover, for any positive vector d in W, the stationary points of [psi] are preserved under the change of variable x < Dx, where D = diag(d). In particular, if d [epsilon] W is a positive constrained stationary point of [psi] corresponding to [formula], where e[superscript (k)] is the vector of k ones, then [formula], where P[subscript d] is the orthogonal projection matrix with respect to the subspace [formula], and [phi][subscript d](x) = [phi](Dx)
4 editions published between 1989 and 1993 in English and held by 10 WorldCat member libraries worldwide
We prove that either [phi] has a nonnegative zero x in W each of whose component vectors x[superscript (j)] [epsilon] W[subscript j], is nontrivial, or, given an admissible [lambda], the logarithmic barrier function [formula], has a positive constrained stationary point in W, and if [phi] is convex, precisely one of these conditions is satisfied. Moreover, for any positive vector d in W, the stationary points of [psi] are preserved under the change of variable x < Dx, where D = diag(d). In particular, if d [epsilon] W is a positive constrained stationary point of [psi] corresponding to [formula], where e[superscript (k)] is the vector of k ones, then [formula], where P[subscript d] is the orthogonal projection matrix with respect to the subspace [formula], and [phi][subscript d](x) = [phi](Dx)
Transactions on computational science XX : special issue on Voronoi diagrams and their applications by
Marina L Gavrilova(
Book
)
8 editions published in 2013 in English and held by 9 WorldCat member libraries worldwide
This, the 20th issue of the Transactions on Computational Science journal, edited by Bahman Kalantari, is devoted to the topic of Voronoi Diagrams and their applications. The 10 full papers included in the volume are revised and extended versions of a selection of papers presented at the International Symposium on Voronoi Diagrams 2012, held in Rutgers, NJ, USA, in June 2012. They provide an indepth overview of current research on topological data structures and a comprehensive evaluation of their applications in the fields of cartography, physics, material modeling, chemistry, GIS, motion planning and computer graphics
8 editions published in 2013 in English and held by 9 WorldCat member libraries worldwide
This, the 20th issue of the Transactions on Computational Science journal, edited by Bahman Kalantari, is devoted to the topic of Voronoi Diagrams and their applications. The 10 full papers included in the volume are revised and extended versions of a selection of papers presented at the International Symposium on Voronoi Diagrams 2012, held in Rutgers, NJ, USA, in June 2012. They provide an indepth overview of current research on topological data structures and a comprehensive evaluation of their applications in the fields of cartography, physics, material modeling, chemistry, GIS, motion planning and computer graphics
A generalized hypergreedy algorithm for perfect matching by Celina Imielinska(
Book
)
2 editions published in 1991 in English and held by 6 WorldCat member libraries worldwide
Abstract: "We give a generalization of the hypergreedy algorithm for minimum weight perfect matching on a complete edge weighted graph K(V) satisfying the triangle inequality, where V is a set of an even number, n, of vertices. We define a heuristic, called the thypergreedy, where t is an integer parameter satisfying [formula], which produces an approximate solution whose edges weight is bounded above by (2t + 1) times the optimal weight. Its time complexity is [formula]. For points in the Euclidean plane, the thypergreedy can be modified to produce an approximate solution, whose weight is bounded above by [squareroot 10](2t + 1) times the optimal weight
2 editions published in 1991 in English and held by 6 WorldCat member libraries worldwide
Abstract: "We give a generalization of the hypergreedy algorithm for minimum weight perfect matching on a complete edge weighted graph K(V) satisfying the triangle inequality, where V is a set of an even number, n, of vertices. We define a heuristic, called the thypergreedy, where t is an integer parameter satisfying [formula], which produces an approximate solution whose edges weight is bounded above by (2t + 1) times the optimal weight. Its time complexity is [formula]. For points in the Euclidean plane, the thypergreedy can be modified to produce an approximate solution, whose weight is bounded above by [squareroot 10](2t + 1) times the optimal weight
Diagnonal [i.e. diagonal] matrix scaling and linear programming by Leonid Khachiyan(
Book
)
3 editions published in 1990 in English and held by 6 WorldCat member libraries worldwide
Abstract: "A positive semidefinite symmetric matrix either has a nontrivial nonnegative zero, or, can be scaled by a positive diagonal matrix into a doubly quasi stochastic matrix. In this paper we describe a simple path following Newton algorithm [sic] of the complexity [formula] iterations to either scale an n by n matrix or give a nontrivial nonnegative zero. The latter problem is wellknown to be equivalent to linear programming."
3 editions published in 1990 in English and held by 6 WorldCat member libraries worldwide
Abstract: "A positive semidefinite symmetric matrix either has a nontrivial nonnegative zero, or, can be scaled by a positive diagonal matrix into a doubly quasi stochastic matrix. In this paper we describe a simple path following Newton algorithm [sic] of the complexity [formula] iterations to either scale an n by n matrix or give a nontrivial nonnegative zero. The latter problem is wellknown to be equivalent to linear programming."
On the complexity of nonnegative matrix scaling by
Bahman Kalantari(
Book
)
2 editions published in 1990 in English and held by 6 WorldCat member libraries worldwide
Abstract: "An n x n nonnegative matrix is said to be (doubly stochastic) scalable if there exists two positive diagonal matrices X and Y such that XAY is doubly stochastic. We derive an upper bound on the norms of the scaling factors X and Y and give a polynomial time complexity bound on the problem of computing the scaling factors with prescribed accuracies."
2 editions published in 1990 in English and held by 6 WorldCat member libraries worldwide
Abstract: "An n x n nonnegative matrix is said to be (doubly stochastic) scalable if there exists two positive diagonal matrices X and Y such that XAY is doubly stochastic. We derive an upper bound on the norms of the scaling factors X and Y and give a polynomial time complexity bound on the problem of computing the scaling factors with prescribed accuracies."
A simple polynomial time algorithm for a convex hull problem equivalent to linear programming by
Bahman Kalantari(
Book
)
2 editions published in 1993 in English and held by 6 WorldCat member libraries worldwide
Abstract: "Over the rationals, the general linear programming problem is equivalent to the convex hull problem of determining if a given m x n matrix H has a nontrivial nonnegative zero. We give a polynomial time algorithm that either finds a nontrivial nonnegative zero of H, or it obtains a hyperplane separating the column vectors of H from the origin. In particular, the algorithm provides an alternate proof of a strengthened version of Gordan's duality theorem, previously proved by the author. The algorithm which is motivated by this duality theorem is analogous to Karmarkar's algorithm but its analysis is much simpler."
2 editions published in 1993 in English and held by 6 WorldCat member libraries worldwide
Abstract: "Over the rationals, the general linear programming problem is equivalent to the convex hull problem of determining if a given m x n matrix H has a nontrivial nonnegative zero. We give a polynomial time algorithm that either finds a nontrivial nonnegative zero of H, or it obtains a hyperplane separating the column vectors of H from the origin. In particular, the algorithm provides an alternate proof of a strengthened version of Gordan's duality theorem, previously proved by the author. The algorithm which is motivated by this duality theorem is analogous to Karmarkar's algorithm but its analysis is much simpler."
High order iterative methods for approximating square and cube roots by
Bahman Kalantari(
Book
)
2 editions published in 1993 in English and held by 6 WorldCat member libraries worldwide
Abstract: "In this paper we describe high order iterative methods for computing the qth root of a given [alpha]> 0, q = 2,3. Given any natural number m [> or =] 2, and any initial approximation x₀> [q root of alpha], we construct a rational function g[subscript m](x) so that the fixedpoint iteration x[subscript k+1] = g[subscript m](x[subscript k]), has an mth order monotonic rate of convergence to [alpha]. In particular for m=2, g₂(x) coincides with Newton's function N(x) = x  p(x)/p'(x), where p(x) = x[superscript q]  [alpha]. For approximation of square roots, parallel implementation of these high order methods allow an asymptotic speedup factor of 3 over Newton's method."
2 editions published in 1993 in English and held by 6 WorldCat member libraries worldwide
Abstract: "In this paper we describe high order iterative methods for computing the qth root of a given [alpha]> 0, q = 2,3. Given any natural number m [> or =] 2, and any initial approximation x₀> [q root of alpha], we construct a rational function g[subscript m](x) so that the fixedpoint iteration x[subscript k+1] = g[subscript m](x[subscript k]), has an mth order monotonic rate of convergence to [alpha]. In particular for m=2, g₂(x) coincides with Newton's function N(x) = x  p(x)/p'(x), where p(x) = x[superscript q]  [alpha]. For approximation of square roots, parallel implementation of these high order methods allow an asymptotic speedup factor of 3 over Newton's method."
High order iterative methods for approximating roots of polynomials by
Bahman Kalantari(
Book
)
2 editions published in 1993 in English and held by 6 WorldCat member libraries worldwide
Abstract: "Let p(x) be a polynomial of degree n [> or =] 2 with real coefficients, and K the field of rationals with the adjunction of the coefficients of p. For any natural number m [> or =] 2, we prove the existence of n rational functions g[subscript m](x), and [gamma][subscript i](x), i = m ..., (m+n2), with coefficients in K so that for all roots [theta] of p(x) we have, [formula]. Furthermore, if p(x) is irreducible over K, g[subscript m](x) is unique. The corresponding fixedpoint iteration, x[subscript k+1] = g[subscript m](x[subscript k]), results in high order of convergence to roots of p(x). In particular, for m = 2, we obtain an explicit formula for g₂(x) and prove that it coincides with Newton's function N(x) = x  p(x)/p'(x). This formula which is derived algebraically gives a new representation of N(x), as well as new interpretation of Newton's method. Except possibly for a finite set of points whose characterization will be given, the fixedpoint iteration is welldefined. Using this characterization we also prove the uniqueness of g[subscript m](x), given that p(x) has n distinct real roots."
2 editions published in 1993 in English and held by 6 WorldCat member libraries worldwide
Abstract: "Let p(x) be a polynomial of degree n [> or =] 2 with real coefficients, and K the field of rationals with the adjunction of the coefficients of p. For any natural number m [> or =] 2, we prove the existence of n rational functions g[subscript m](x), and [gamma][subscript i](x), i = m ..., (m+n2), with coefficients in K so that for all roots [theta] of p(x) we have, [formula]. Furthermore, if p(x) is irreducible over K, g[subscript m](x) is unique. The corresponding fixedpoint iteration, x[subscript k+1] = g[subscript m](x[subscript k]), results in high order of convergence to roots of p(x). In particular, for m = 2, we obtain an explicit formula for g₂(x) and prove that it coincides with Newton's function N(x) = x  p(x)/p'(x). This formula which is derived algebraically gives a new representation of N(x), as well as new interpretation of Newton's method. Except possibly for a finite set of points whose characterization will be given, the fixedpoint iteration is welldefined. Using this characterization we also prove the uniqueness of g[subscript m](x), given that p(x) has n distinct real roots."
New optimality conditions and algorithms for homogeneous and polynomial optimization over spheres by
A Bagchi(
Book
)
2 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
In particular, we propose an inherently simple procedure for the trust region problem, where a quadratic form plus a linear term is optimized over a sphere. For such problems, it is known that a boundary point is a global minimum if and only if it satisfies the first order condition and a stronger second order condition. We give an alternative proof of this fact using saddle point theory. We also derive an additional second order condition using the homogeneous optimization theory developed above."
2 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
In particular, we propose an inherently simple procedure for the trust region problem, where a quadratic form plus a linear term is optimized over a sphere. For such problems, it is known that a boundary point is a global minimum if and only if it satisfies the first order condition and a stronger second order condition. We give an alternative proof of this fact using saddle point theory. We also derive an additional second order condition using the homogeneous optimization theory developed above."
On the rate of convergence of the RAS method by
Bahman Kalantari(
Book
)
2 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Abstract: "It is wellknown that given an n x n matrix with positive entries, there exists two positive diagonal matrices X and Y such that XAY is doubly stochastic. One of the best known algorithms for computing the scaling factors X and Y is the so called RAS algorithm which alternatively normalizes rows and columns of the matrix. In this paper we prove that the RAS is a fullypolynomial time approximation scheme and give a bound of O((1/[epsilon] + ln n) [squareroot n]ln 1/v), on the number of iterations of the RAS for scaling A to an accuracy of [epsilon], where v is the ratio of the least entry of A to its largest."
2 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Abstract: "It is wellknown that given an n x n matrix with positive entries, there exists two positive diagonal matrices X and Y such that XAY is doubly stochastic. One of the best known algorithms for computing the scaling factors X and Y is the so called RAS algorithm which alternatively normalizes rows and columns of the matrix. In this paper we prove that the RAS is a fullypolynomial time approximation scheme and give a bound of O((1/[epsilon] + ln n) [squareroot n]ln 1/v), on the number of iterations of the RAS for scaling A to an accuracy of [epsilon], where v is the ratio of the least entry of A to its largest."
Quadratic functions with exponential number of local maxima by
Bahman Kalantari(
Book
)
5 editions published between 1985 and 1986 in English and held by 5 WorldCat member libraries worldwide
5 editions published between 1985 and 1986 in English and held by 5 WorldCat member libraries worldwide
A good heuristic for the Chinese postman problem by M. D Grigoriadis(
Book
)
2 editions published in 1985 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1985 in English and held by 4 WorldCat member libraries worldwide
Solving linear programs in the standard form by bisection and a projective feasability algorithm by
Bahman Kalantari(
Book
)
5 editions published in 1987 in English and held by 4 WorldCat member libraries worldwide
5 editions published in 1987 in English and held by 4 WorldCat member libraries worldwide
Ninth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD), 2012 2729 June 2012, Rutgers, the State
University of New Jersey, Busch Campus in Piscataway(
)
1 edition published in 2012 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2012 in English and held by 4 WorldCat member libraries worldwide
On the existence of weak greedy matching heuristics by M. D Grigoriadis(
Book
)
2 editions published between 1985 and 1986 in English and held by 4 WorldCat member libraries worldwide
2 editions published between 1985 and 1986 in English and held by 4 WorldCat member libraries worldwide
Minimum cost network flow problem on spanning trees and 1trees by
Bahman Kalantari(
Book
)
3 editions published in 1987 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1987 in English and held by 4 WorldCat member libraries worldwide
A general class of heuristics for minimum weight perfect matching and a log₃ log₃ nerror special case in O(n²loglogn)time by Celina Imielinska(
Book
)
2 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
It is also possible to use our heuristic to obtain a solution with an error of 5.2(log₃ n)[superscript 0.25] in O(n²) time."
2 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
It is also possible to use our heuristic to obtain a solution with an error of 5.2(log₃ n)[superscript 0.25] in O(n²) time."
Generalization of Karmarkar's algorithm to convex homogeneous functions by
Bahman Kalantari(
Book
)
2 editions published in 1989 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1989 in English and held by 4 WorldCat member libraries worldwide
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Related Identities
 Gavrilova, Marina L. Author Editor
 Tan, C. J. Kenneth (Chih Jeng Kenneth) Editor
 Rutgers University Department of Computer Science
 Kalantari, Iraj
 Khachiyan, Leonid Author
 Imielinska, Celina Author
 Grigoriadis, M. D. Author
 Rutgers University
 Bagchi, A. Author
 Khachiyan, Leonid G. Author
Associated Subjects
Algorithms Approximation theory Artificial intelligence Computer graphics Computer science Computer scienceMathematics Computer vision Geometry Graph theory Heuristic Heuristic programming Linear programming Linear programmingData processing Matching theory Mathematical optimization Matrices Nonnegative matrices Numerical analysis Polynomials Quadratic programming Quadratic programmingData processing Recurrent sequences (Mathematics) Trees (Graph theory) Vector valued functions Visualization Voronoi polygons