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	Narendra Karmarkar at AllExperts
		The significance of his invention lies in the fact that it was the first algorithm to solve linear programming problems which had a good running time both theoretically and in practice.
		Karmarkar received his B.Tech at the IIT Bombay in 1978.
		Today Karmarkar has a professor position at the Tata Institute of Fundamental Research in Bombay.
	en.allexperts.com /e/n/na/narendra_karmarkar.htm (401 words)

	United States Patent: 4,914,563
		Karmarkar describes two related "rescaling" transformations for moving a point to the center of the polytope.
		The advantages of the Karmarkar invention derive primarily from the fact that each step is radial within the polytope rather than circumferential on the polytope surface and, therefore, many fewer steps are necessary to converge on the optimum point.
		Still, even in Karmarkar's method and apparatus a substantial number of iterations is required when the number of variables to be controlled is very large.
	laniels.org /cache/karmarkar_algorithm.html (8582 words)

	The Mathematical Tourist
		Karmarkar's algorithm boldly jumps away from the concept of a surface path zigzagging from vertex to vertex on a polytope of fixed shape.
		Like the ellipsoid method, Narendra Karmarkar's scheme also runs in polynomial time, but the exponent governing how long his method takes is smaller than the exponent governing the ellipsoid method.
		Karmarkar's method pushes up the number of variables and constraints that can be handled within a reasonable time.
	www.fortunecity.com /emachines/e11/86/tourist4e.html (1791 words)

	Science News: A linear programming race. @ HighBeam Research (Site not responding. Last check: 2007-10-13)
		In 25 cases, the Karmarkar method found the answer faster than a version of the simplex method running on the same computer.
		The Karmarkar method ran significantly faster on larger problems, but even for small problems and in a few special cases, this method was only a little slower.
		Writing in the current issue of AT&T's RECORD, Karmarkar and his colleagues report, "Although [the algorithm's] full capabilities and limitations are still being explored, its ability to greatly reduce computation times for some large practical problems has already been demonstrated." However, AT&T has thus far refused to make its implementation public.
	www.highbeam.com /library/doc0.asp?DOCID=1G1:4277501&refid=ip_encyclopedia_hf (402 words)

	Definition of Narendra Karmarkar
		Narendra Karmarkar (born 1957) is an Indian mathematician.
		In 1984 he discovered what is now known as Karmarkar's algorithm, while working at Bell Laboratories in New Jersey.
		Karmarkar received his B.Tech degree from IIT Bombay in 1978.
	www.wordiq.com /definition/Narendra_Karmarkar (193 words)

	Narendra Karmarkar - Encyclopedia Glossary Meaning Explanation Narendra Karmarkar (Site not responding. Last check: 2007-10-13)
		Narendra Karmarkar - Encyclopedia Glossary Meaning Explanation Narendra Karmarkar.
		Here you will find more informations about Narendra Karmarkar.
		Together, these contributions inspired a renaissance in the theory and practice of linear programming, leading to orders of magnitude improvement in the effectiveness of widely-used commercial optimization codes.
	www.encyclopedia-glossary.com /en/Narendra-Karmarkar.html (197 words)

	IITBHF and IITBAA (http://www.iitbombay.org)
		In 1984, Narendra Karmarkar (BTech EE '78) made a groundbreaking discovery in the field of Linear Programming while working at the famed Bell Labs in New Jersey.
		In 1984, Narendra Karmarkar introduced an interior-point method for linear programming, combining the desirable theoretical properties of the ellipsoid method and practical advantages of the simplex method.
		Narendra Karmarkar Citation For his theoretical work in devising an Interior Point
	www.iitbombay.org /misc/press/karmarkar.htm (728 words)

	Distinguished Alumnus 1996 (Site not responding. Last check: 2007-10-13)
		Narendra Karmarkar is well-known for the Karmarkar algorithm for linear programming which was announced in 1984 and which made headlines not onlyu in scientific publications but also the mass media.
		Karmarkar had the distinction of receiving the Marconi International Young Scientis Award in 1985 and the Fulkerson Prize in discrete mathematics given jointly by the American Mathematical Society and Mathematical Programming Society in 1988.
		Karmarkar is regularly invited to make presentations in important international conference in his field of interest.
	www.alumni.iitb.ac.in /dist_alu_1996.htm (2900 words)

	Indian Express: Focus on high end computing (Site not responding. Last check: 2007-10-13)
		PUNE, June 4: Senior professor at the Tata Institute of Fundamental Research (TIFR) Narendra Karmarkar today said it was not enough for the country to merely supply the labour component in the rapidly moving IT industry.
		Karmarkar was delivering the key-note address on the topic ``IT revolution and the role of mathematical programming,'' at the two day seminar - ``Update 99'' organised by the Software Technology Parks of India (STPI) to mark the ninth Foundation Day.
		Billions of dollars are expected storing and distributing current technologies for storing road advances in data gathering, storing and distribution, he said, adding that new technologies outpaced the existing ones in converting the raw data into actionable information.
	www.expressindia.com /ie/daily/19990605/ige05131p.html (456 words)

	DBLP: Narendra Karmarkar (Site not responding. Last check: 2007-10-13)
		Narendra Karmarkar, Yagati N. Lakshman: On Approximate GCDs of Univariate Polynomials.
		Narendra Karmarkar, Yagati N. Lakshman: Approximate Polynomial Greatest Common Divisors and Nearest Singular Polynomials.
		Narendra Karmarkar, Richard M. Karp, Richard J. Lipton, László Lovász, Michael Luby: A Monte-Carlo Algorithm for Estimating the Permanent.
	www.informatik.uni-trier.de /~ley/db/indices/a-tree/k/Karmarkar:Narendra.html (235 words)

	Narendra III - Encyclopedia Glossary Meaning Explanation Narendra III (Site not responding. Last check: 2007-10-13)
		Narendra III - Encyclopedia Glossary Meaning Explanation Narendra III.
		Here you will find more informations about Narendra III.
		The gallant actions of the Enterprise-C helped further cement the good relations formed between the Federation and the Klingon Empire stemming from the Khitomer Accords, and lasted until a rift formed between the 2 over the Empire's invasion of Cardassian space.
	www.encyclopedia-glossary.com /en/Narendra-III.html (188 words)

	CITIDEL: Viewing 'A new parallel architecture for sparse matrix computation based on finite projective geometries' (Site not responding. Last check: 2007-10-13)
		Dhillon, I. Karmarkar, N. and Ramakrishnan, K. G., An Overview of the Compilation Process for a New Parallel Architecture, Proceedings of the Fifth Canadian Supercomputing Conference, Fredericton, N.B., Canada, June 1991.
		Karmarkar, N. A New Parallel Architecture for Sparse Matrix Computations, Proceedings of the Workshop on Parallel Processing, BARC, Bombay, February 1990, pp.
		Karmarkar, N., A New Parallel Architecture for Sparse Matrix Computations Based on Finite Projective Geometries, invited talk at the SIAM Conference on Discrete Mathematics, Atlanta, June 1990.
	www.citidel.org /?op=getobj&identifier=oai:ACMDL:articles.126029 (343 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Karmarkar's method (as described in his original paper in Combinatorica (1984) contains some innovative ideas that serve mostly to advance the proof that the algorithm is polynomial.
		Karmarkar's exact method is more mathematically subtle, but correspondingly less practical.
		The claims made by Karmarkar and AT&T for their implementation in 1984 were certainly inflated.
	www.cs.cmu.edu /afs/cs.cmu.edu/academic/class/15850c-s96/www/interiorpoint.txt (3866 words)

	Narendra Karmarkar biography .ms (Site not responding. Last check: 2007-10-13)
		In 1984 he discovered what is now known as Karmarkar's algorithm, while working at Bell Laboratories in New Jersey.
		The Association for Computing Machinery awarded him the prestigious Paris Kanellakis Award for his work.
		Karmarkar received his B.Tech degree from Bombay IIT in 1978.
	narendra-karmarkar.biography.ms (121 words)

	IITBHF and IITBAA (http://www.iitbombay.org)
		In 1984, Narendra Karmarkar (BTech EE '78) made a groundbreaking discovery in the field of Linear Programming while working at the famed Bell Labs in New Jersey.
		In 1984, Narendra Karmarkar introduced an interior-point method for linear programming, combining the desirable theoretical properties of the ellipsoid method and practical advantages of the simplex method.
		Narendra Karmarkar Citation For his theoretical work in devising an Interior Point
	www.iitmumbai.org /misc/press/karmarkar.htm (728 words)

	An Implementation Of Karmarkar's Algorithm For Linear Programming - Adler, Karmarkar, Resende, Veiga (ResearchIndex) (Site not responding. Last check: 2007-10-13)
		Based on a continuous version of Karmarkar's algorithm, two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested.
		Linear programs are expressed in an inequality form, which allows for the inexact computation of the algorithm's direction of improvement, resulting in a significant computational...
		1 An extension of Karmarkar (context) - Todd, Burrell - 1986
	citeseer.ist.psu.edu /173633.html (676 words)

	A prime solution
		One would recall the discovery of an exciting algorithm by another Indian scientist Narendra Karmarkar, then working in the U.S. (currently in Pune) in the area of linear programming.
		In some sense, this work is much superior to that in the sense that first the complexity in the prime number problem is much more, and in terms of polynomial time achieved, the Karmarkar algorithm is much less efficient, according to computer science experts.
		Karmarkar's algorithm had been touted to generate a great deal of revenue and that the patent on it would generate huge royalty for Bell Labs.
	www.flonnet.com /fl1917/19171290.htm (2831 words)

	Narendra Karmarkar Bags the Only A by M.S. Kamath
		He was quoted as saying, "I used to tell my students, 'IIT is a center of excellence.
		It was no surprise that Narendra Karmarkar got an A on Kamath's course.
		Karmarker had missed out on a few As during the first year but after that, except for a few humanities courses, consistently received As in almost all his courses, finally receiving the President's Gold medal for graduating with the highest GPA of our batch.
	www.kamalsinha.com /iit/essays/grading.html (1031 words)

	ie6933syllabus
		Karmarkar's LP algorithm attracted considerable attention in the scientific community, and even the popular press, due to Karmarkar's claims of massive speedups, typically by factors of 10-50, compared with the times required by the simplex method on large linear programs.
		Although disagreement over Karmarkar's solution times immediately ensued, all experimental evidence indicated that the new algorithm required a relatively small number of iterations, typically 30-60, to obtain near-optimal solutions to linear programs of virtually any size.
		The fact that problems with tens of thousands of variables required roughly the same number of iterations as problems with a few hundred variables indicated that the method had tremendous practical potential, at least for large-scale linear programming.
	students.ou.edu /I/Huseyin.Ince-1/ie6933syllabus.htm (614 words)

	Method and apparatus for optimizing system operational parameters - Patent 4744027
		373-395, and the affine scaling method is described in the aforementioned N. Karmarkar application Ser.
		Transforming a general statement of the optimization task (e.g., in the form Ax.ltoreq.b) to the canonical form of equation (2) can be done in accordance with prior art techniques, such as the one described in Section 5 of an article by N. Karmarkar entitled "A New Polynomial-Time Algorithm for Linear Programming," Combinatorica 4 (4), pp.
		A second method for determining a step size is to minimize the "potential function" of Karmarkar, defined by ##EQU10## on the line segment connecting e (the starting point of the iteration) and y'.sub.1 (the trial tentative allocation), to obtain a point y.sub.1.
	www.freepatentsonline.com /4744027.html (8500 words)

	Rediff On The NeT: Renowned mathematician Narendra Karmarkar returns home, joins TIFR
		Dr Narendra Karmarkar, the internationally acclaimed mathematician, has joined the Tata Institute of Fundamental Research, Bombay.
		Dr Karmarkar will be responsible for setting up an independent department of computer-oriented mathematics at TIFR.
		As procedural formalities are pending, Dr Karmarkar said he would comment on his appointment only after the TIFR board met on September 16.
	www.rediff.com /news/aug/30tata.htm (221 words)

	I am interested in broad areas of Computer Science (Site not responding. Last check: 2007-10-13)
		Narendra Karmarkar (mentor in summer internship in Tata Institute of Fundamental Research, India)
		I returned from Duluth to Pune to work with Dr. Narendra Karmarkar as a part of my summer internship.
		The entire area of arbitrary precision arithmetic was new to me. In the 3 months of internship I used FMLIB and ported the CML code to run with FMLIB.
	www-users.cs.umn.edu /~dkulk/Research.htm (812 words)

	AT&T News Release, 1993-08-30, AT&T IMS division merges two operations research groups (Site not responding. Last check: 2007-10-13)
		This group is the 1993 winner of prestigious Franz Edelman Award for Management Science Achievement, sponsored by the In- stitute of Management Science (TIMS).
		The Karmarkar algorithm, upon which early ADSS products were based, is a linear programming algorithm created by Dr. Narendra Karmarkar of AT&T Bell Laboratories.
		Hailed as the breakthrough sought by the international mathematics community for more than 40 years, it is widely recognized as the most highly advanced mathematical optimization tool ever devised.
	www.att.com /news/0893/930830.chb.html (366 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Commenting on the first computer, the Param 10000, Dr Narendra Karmarkar, Head (CML), TIFR, said the Param was a 32-bit processor and operating system while the TIFR would have a 64-bit processor and operationg system.
		The switch over from 32-bit to 64-bit has been happening in the US for some time while noting that this was the first in India.
		Dr Narendra also pointed out that India needed to invest much more in the HPC area while noting that the country could boast of the correct hardware, software engineers, mathematical brains which would be teamed up with the expertise brought in from HP.
	www.hinduonnet.com /thehindu/thscrip/print.pl?file=2005042100651900.htm&date=2005/04/21/&prd=bl& (329 words)

	Linear Independence
		Summer 1984 brought the announcement by Narendra Karmarkar, a mathematician at ATandT Bell Laboratories, of a new algorithm, claimed to be significantly faster than the simplex algorithm.
		Speed is crucial in some applications of LP to large problems, such as rescheduling airlines when severe weather disrupts regular schedules.
		68.) Regardless of the outcome of the controversy, the excitement caused by Karmarkar's algorithm shows that mathematics and linear algebra are far from cut-and-dried disciplines; they are growing, living fields of study and application.
	distance-ed.math.tamu.edu /Math640/chapter7/node6.html (874 words)

	Modern Algorithms (Site not responding. Last check: 2007-10-13)
		In 1985, Bell Labs researcher Narendra Karmarkar found a way to mathematically leap across boundaries instead of following that line.
		A simplex algorithm is like driving an interstate from one city to another; a Karmarkar algorithm is like flying there.
		Bill Pulleyblank, who develops algorithms at IBM's Watson Research Centre has stated, "A lot of algorithm development is not breakthrough work, you do better a little at a time." One painstaking method is to run an algorithm on a computer, detail how long each calculation takes, then work on each one to make it faster.
	www.veritus.org /scndtier/algorith.php (619 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Conference Announcement: FOUNDATIONS of COMPUTATIONAL MATHEMATICS IMPA, Rio de Janeiro, January 5-12, 1997 The reaction to the Park City meeting on Mathematics of Numerical Analysis: Real Number Algorithms which was chaired by Steve Smale and which had around 275 participants was very enthusiastic.
		At the suggestion of Narendra Karmarkar we have decided to try to hold an annual or perhaps biannual meeting entitled "Foundations of Computational Mathematics" and to form an organization with the same name whose primary purpose will be to hold the meeting.
		A lunch time meeting of Felipe Cucker, Arieh Iserles, Narendra Karmarker, Jim Renegar, Mike Shub and Steve Smale asked Mike Shub to act on its behalf.
	nalab.is.tsukuba.ac.jp /~itosho/cgi-bin/97-01/RIODEJANEIRO.97-01.html (287 words)

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