Narendra Karmarkar Contribution To Mathematics

Narendra Karmarkar was born in the Gwalior to a small middle class Marathi family. Narendra Karmarkar had received his B.Tech in the Electrical Engineering from the IIT Mumbai in 1978. He had completed his M.S from the famous California Institute of University and completed his Ph.D. in the Computer Science from the famous University of California, Berkeley. He had published his most famous result in 1984 while he was then working for the Bell Laboratories in the New Jersey. Narendra Karmarkar was a famous professor at the Tata Institute of Fundamental Research located in Mumbai. He is currently now working on a very new architecture used for supercomputing. Some of the ideas that are published at the Fab5 conference which is organised by the MIT center for the bits and atoms.

Karmarkar’s Famous algorithm
Karmarkar’s algorithm solves the various linear Programming problems in the polynomial time. These problems are mostly represented by a “n” variables and a “m” constraints. The previous used method for solving these type of problems consisted a lot of problem representation by a “x” sided solid with a “y” vertices, where all the solution was then approached by traversing it from the vertex tovertex. Karmarkar’s novel method approaches all the solution by method of cutting through the all the above solid in all its traversal. Consequently, the complex optimization problems are also solved much faster using the method of Karmarkar algorithm. A practical example of this type of efficiency is the solution to a very complex problem in the communications network optimization where all the solution time taken was reduced from the weeks to some days. His algorithm thus enables the faster business and various policy decisions. Karmarkar’s algorithm has also stimulated all the development of the several other used interior point methods, some of which are now used in the current codes for solving the linear programs.

Current investigations
Currently, he is focusing on synthesizing these types of concepts with some brand new ideas that he calls sculpturing free space (a non-linear analogue of what now has popularly been described as folding all the perfect corner). This type of approach allows him to extend all this work to a physical design of various machines. He is now teying publishing updates on all his recent task, including an extended type of abstract. This new paradigm was first presented at the INVC Poland on 16 July 2008, and at the MIT on the 25 July2008. Some of the most recent work of his is published at the Fab5 conference which is organized by the MIT center for the bits and atoms

Author: Arya Math

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