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SYAMAL KUMAR SEN                                                     
Professor, Department of Mathematical Sciences
Florida Institute of Technology
                                                                                       




PRINCIPAL RESEARCH INTERESTS

There exists no noniterative polynomial-time algorithm for solving linear programs (LPs). A new O(n3) algorithm (polynomial-time) which is noniterative heuristic has been designed and developed. This algorithm which is almost like obtaining a solution of linear equations has been found to be extremely useful in solving most linear programming problems. Even if an optimal solution is not reached, the algorithm does produce one close to it, has an inherent test for optimality, as well as can be used as an excellent preprocessor that needs no artificial variables. An error-free version of this algorithm that gives exact optimal solution for most linear programs has also been developed. The open problem of either developing a noniterative polynomial-time deterministic algorithm or proving the nonexistence of such an algorithm is being attempted.
Several methods are available for solving linear (ordinary and partial) differential equations with linear boundary conditions. There are inherent problems in obtaining a best solution and also in ascertaining the quality of the solution. Often this solution could be biased. Under these circumstances, we have obtained a best solution of linear partial/ordinary differential equations in the minimum-norm least-squares sense. This solution is unbiased and has a built-in narrow relative error-bound that assures the quality of the result.
An interior-point method called here the polytope-shrinking algorithm has been developed to solve linear programs. It has a very simple way to compute a centre of the polytope and has a simple technique to proceed in the direction of the optimal solution.This algorithm is iterative and promising. Its computational complexity is being attempted.
A concise near-consistent linear system solver, different from a least-squares solution or a minimum-norm least-squares solution, along with a measure of inconsistency and a sharp relative error-bound has been developed. This algorithm is very useful for solving overdetermined linear system arising out of linear differential equations (partial/ordinary) and multiple regression models. The solver is being attempted for large sparse and dense systems in a distributed computing environment.

RESEARH ARTICLES

BOOKS

1. V. Lakshmikantham; S.K. Sen, Computational Error and Complexity in Science and Engineering,  Elsevier, Amsterdam as Volume 201  under the Series Mathematics in Science and Engineering (edited by C.K. Chui, Stanford University), 260 pages, 229 mm X 152 mm, 2005.

2. E.V. Krishnamurthy; S.K. Sen, Introductory Theory of Computer Science,  Affiliated East Press, New Delhi, 274 + x, pages, 2004.

3. book1 Introductory Theory of Computer Science (with E.V. Krishnamurthy), Affiliated East Press, New Delhi, 274 + x, pages, 2004.

 

MONOGRAPH

1.  book2Computational Error and Complexity in Science and Engineering (with V. Lakshmikantham), Elsevier, Amsterdam, as Volume 201  under the Series Mathematics in Science and Engineering (edited by C.K. Chui, Stanford University), 260 pages, 229 mm X 152 mm, 2005.



BOOK CHAPTERS

1. S.K. Sen, Formalization of Computation in Nature: An Expository Review, in Mathematics and Information Theory: Recent Topics and Applications, ed. V. K. Kapoor, Anamaya Publisher, New Delhi, 2004, 1-16. 

2. Formalization of Computation in Nature: An Expository Review, in Mathematics and Information Theory: Recent Topics and Applications, ed. V. K. Kapoor, Anamaya Publisher, New Delhi, 2004, 1-16.



Recent Publications

 

1. V. Lakshmikantham, S.K. Sen, and T. Samanta, Comparing  random number generators using Monte Carlo integration, International Journal of Innovative Computing, Information and Control,  1, No. 2, pp. 143-165, June 2005.

2. S.K. Sen; H. Agarwal, Mean value theorem for boundary value problems with given upper and lower solutions, Computers and Mathematics with Applications, 49, 2005, 1499-1514.

3. V Lakshmikantham; S.K. Sen; A. Mohanty, Error in error-free computation for linear system, Neural, Parallel & Scientific Computations, 12,  2004, pp. 113-122.


Others

  1. Yet-to-be solved problems in computational science, to appear, 2005.
  2. 2n in scientific computation and beyond (with Hans Agarwal), accepted for publication in Mathematical and Computer Modelling, 2005.
  3. Open problems in computational linear algebra, accepted for publication in Nonlinear Analysis (Elsevier), 2005 (also presented as an invited talk at the Fourth World Congress of Nonlinear Analysis (WCNA-2004), Orlando, Florida.
  4. O(n3) g-inversion-free noniterative near-consistent  linear system solver for minimum-norm least-squares and nonnegative solutions (with Sagar Sen), accepted for publication and to appear in J. Computational Methods in Sciences and Engineering, 2005.
  5. Relative merits of random number generators: indirect approach (with T. Samanta), accepted for publication in  Nonlinear Analysis 2005 (also presented at the Fourth World Congress of Nonlinear Analysis (WCNA-2004), Orlando, Florida, June 30- July 07, 2004).
  6. Mean value theorem for boundary value problems with given upper and lower solutions (with Hans Agarwal), accepted for publication in Computers and Mathematics with Applications, 2004.
  7. Error in error-free computation for linear system (with V. Lakshmikantham and A. Mohanty), 2004, to appear, 2005.

 

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