SYAMAL KUMAR
SEN
Professor, Department of Mathematical
Sciences
Florida Institute of Technology
SHORT BIOGRAPHY
Syamal
Kumar Sen received a B. Sc. (Hons.). (Physics) degree from the
Professor
Sen’s research has spanned a number of
disciplines, emphasizing computational science/mathematics. Concurrently, he
contributed to several fields of mathematics, especially quasi- and
pseudo-random number generators: their scope, probabilistic algorithms,
numerical analysis, computational error and complexity including error in
error-free computations, and computational linear algebra. He has coauthored
several books, including Computational
Error and Complexity in Science and Engineering (with V. Lakshmikantham),
Elsevier, 2005, Introductory Theory of
Computer Science (with E.V. Krishnamurthy), Affiliated East-West Press,
2004, and Numerical Algorithms:
Computations in Science and Engineering (with E.V. Krishnamurthy),
Affiliated East-West Press, 2001. In the course of his research and teaching,
Professor Sen has mentored several doctoral students. He authored/ co-authored
over 139 journal papers, book
chapters, books, and monograph (129 published scientific journal papers, 3
published scientific book-chapters, 6 published scientific books, and 1 scientific
monograph). In addition, he has authored 12 unpublished research articles, at
least 11 published general literary articles in both English and Bengali
languages, at least 7 scientific lecture notes. Number of all these
publications is as on Jan 30, 2008.
Professor
Sen held Fulbright fellowship (for
senior teachers). He served as member/chairman of Expert Committees for various
universities, institutes, and national organizations for the
selection/appointment of faculty/official at a senior level. He is
cited/included in Marquis Who’s
Who (Sep 2005)
CURRENT BOOK/BOOK CHAPTER PUBLISHING ACTIVITIES (2001-2005:
SELECTED ONES)
BOOKS
- Introductory
Theory of Computer Science, Affiliated East Press,
- Numerical
Algorithms: Computations in Science and Engineering (E.V.
Krishnamurthy), Affiliated East-West Press, New Delhi, 629 +
xxii pages, 18 cm ´ 24 cm, 1986 (subsidized by Government of
India through National Book Trust, India for the benefit of students) for
mainly graduate and research students. This book has been reprinted
in 1989 and further reprinted with the addition of significant materials
on parallel computing several modification and inclusions in 1993, in
1996, in 2000, and in 2001 (Used as a text-book in Florida Tech, USA; also
being used in several universities, government institutes as well as
laboratories in India and abroad as a reference/textbook).
MONOGRAPH
1. 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. This monograph
(coauthored with Professor V. Lakshmikantham, Florida Tech,
BOOK CHAPTERS
1.
Error and
Computational Complexity in Engineering, in: Computational Mathematics, Modelling and Algorithms
(Chap. 5) ed. J.C. Misra, Narosa Publishing
House,
2. Linear Programming: Recent Advances, in: Uncertainty and Optimality, Probability, Statistics, and Operations Research, ed. J.C. Misra, World Scientific Publishing, Singapore, 2002, 411-442. This chapter is an overview of recent interior-point methods for linear programs and their scope and includes some of the author’s recent research contributions.
3. 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. This is about an attempt to mimic the natural processes.
CURRENT RESEARCH ACTIVITIES (1996-2006: Selected
Ones)
There exists no non-iterative polynomial-time
algorithm for solving linear programs (LPs). A new O(n3)
algorithm (polynomial-time) which is non-iterative 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 variable. An
error-free version of this algorithm that gives exact optimal solution for most
linear programs has also been developed (Applied
Mathematics and Computation, Elsevier Science Inc.,
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 (Intern
J. Computer Math., Gordon and Breach Science
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 appears to
behave like solving linear system with a computational complexity O(n3) (Neural,
Parallel & Scientific Computations, Dynamic Pub.,
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
over-determined linear system arising out of linear differential equations
(partial/ordinary) and multiple regression models. A system with large
inconsistency is detected as an in-built of this algorithm prompting the
researcher to relook into the mathematical model of
the concerned physical problem. In nature actual physical problem),
inconsistency is unknown (J.
Computational Methods in Sciences and Engineering, to appear) The solver is being attempted for large sparse and dense
systems in a distributed computing environment.
Error-free computation assumes inputs to be exact.
This assumption is incorrect and often not acceptable in real-world
applications. Thus given the error bounds in the input data, what would be the
error bounds in the output results in an error-free environment? A deterministic procedure for the solution of
this problem has a complexity which is combinatorial (exponential) and hence
useless. However, we have derived a polynomial time estimate for the
error-bounds in the outputs when input error-bounds are specified. It may be
seen that it is not difficult to derive/know relatively narrow error-bounds for
the input data since associated with any measuring device there is a fixed
order error (usually of the order of .005%) (Monograph entitled Computational Error and Complexity in Science and
Engineering, Elsevier,
Solving nonlinear ordinary differential equations
associated with two-point boundary conditions and involving singularity and
sensitivity in certain regions (ill-conditioned) is numerically
error-intensive. A mean-value theorem based fast converging algorithm that uses
mathematically derived upper and lower bounds of the solution has been
developed. This is useful in circular membrane problems (Computers and Mathematics with Applications, Pergamon Press,Vol. 49,
2005, 1499—1514). Further developed is another algorithm based on
interpolation for nonlinear boundary-value problems in circular membrane with
known upper and lower solutions. This algorithm also performs well for problems
with singularities and permits visualization of the solution graphically. This
visualization enables one to comprehend the character of the problem nicely (Computers and Mathematics with Applications,
Pergamon Press, 51, 2006, 1021-1046).
Most recently, various quasi-random number and
pseudo-random number generators have been compared and attempt has been made to
determine the scope of these generators (International
Journal of Innovative Computing, Information and Control, Japan, 1, 2005 No. 2, pp. 143-165). Also, discrepancy, complexity, and
integration-error based comparison of quasi- and pseudo random number
generators have been studied along with visualization; pros and cons of both in
solving real world problems have been explored (International Journal of Innovative Computing, Information and Control,
Japan, 2, No. 3, 621-651, June 2006)
Their scope and usage in solving optimization (linear and nonlinear)
problems, traveling salesman’s problems (through polynomial-time
randomized algorithms such as the Simulated Annealing method) are being
explored. In addition, an exhaustive
study on the importance of 2n in scientific computation and beyond
depicting the unique scope of the base-2 number system in the world of numbers
has been carried out (Mathematical and
Computer Modelling, Elsevier, 43, Issues 5 -6,
658-672, March 2006).
An integer program as a mathematical model has
significant real world importance. Its complexity, arithmetic, basic variables,
and scope have been revisited with several application oriented tips (Proc. Neural, Parallel and Scientific
Computations, 3, 237-242, August
2006). A general integer programming method is exponential. Proposed is an
integer programming approach which is polynomial-time and is used for most
chemical equation balancing (Mathematical
and Computer Modelling, Elsevier, 44, Issues 7-8,
678-691, October 2006; also available online at www.sciencedirect.com). For many
intractable (exponential) optimization problems, genetic alrogithms
are attractive propositions since these algorithms are polynomial-time and
hence tractable. Polynomial-time preprocessors with n dimensional bisection have been suggested for genetic algorithms,
which provide an error estimation and are useful in solving real world large
constrained as well as unconstrained optimization problems (Proc. Neural, Parallel and Scientific
Computations, 3, 243-252, August, 2006).
Past Research Activities (Selected Ones)
·During 1986-95
A stable O(n2)
algorithm to solve symmetric singular Toeplitz
systems which occurs in many physical problems was developed. Both from
computational error and complexity point of view, this algorithm is competitive
and suits well for large systems (Nonlinear
World (Walter de Gruyter, New York), Vol. 1, 1994, pp. 429-443). Also stabilized
is Trench’s algorithm to invert near-singular Toeplitz
matrices (Applied Mathematics and
Computation (Elsevier Science Pub. Co.,
In over-under-determined linear systems, we may
have many linearly dependent (both mathematically and numerically) rows which
do not carry any additional information and hence are redundant
. A physically concise algorithm that detects such rows as its in-built
feature and weeds them out before computing the minimum norm least squares
inverse of the shrunken matrix and consequently obtaining the solution vector.
This has dual advantages - less computation and hence less error and less
storage requirement (.Applied
Mathematics and Computation (Elsevier Science Pub. Co.,
Most linear programs with constraints in an
inequality form are solved by converting them to equations increasing the
number of variables, the storage, computation time, and possibly error (e.g.
simplex algorithms, Karmarkar algorithms). This is
done because we have at our disposal a well-established theory of equations and
we can freely and conveniently use the relevant properties of this theory.
However, to obviate these drawbacks, we explored and established an algorithm
that deals straightway with the inequalities and solves the linear programs
iteratively as do most algorithms (J.
Mathematical Analysis and Applications , Academic
Press,
A nonsymmetric eigenvalue problem is more involved than the symmetric one.
A symmetrizer of a given nonsymmetric
matrix, that can be used to produce a symmetric matrix, called by us an
equivalent symmetric matrix, whose eigenvalues are
the same as those of the nonsymmetric matrix is
important since a symmetric matrix eigenvalue problem
is easier to solve. An algorithm to compute such an equivalent symmetric matrix
was developed (Intern. J. Computer Math,, Gordon and Beach Science Publishers, Inc.,
The equation AX + XB = C is occurs in many real
world problems as a mathematical model. And can be ill-conditioned. In this
context, noniterative fail-proof triangularization algorithms
for the equation was developed; an error-free as well as a parallel
implementation have also been achieved (.Applied
Mathematics and Computation (Elsevier Science Pub. Co.,
The solution space of the system Ax = b, x ³ 0 is
called a polytope. A polytope
has no unique center like the that of a sphere. An
interior point method to solve a linear program attempts to procee4d towards
the optimal solution starting from a center and often obtains such a center
using complicated computation. We here developed a simple algorithm to obtain a
center which is good enough as a starting point to proceed towards the
direction of the c vector where the
objective function is ctx (Internat. J. Math. & Math.
Sci., Vol. 16,
2, 1993, pp. 209-224).. In fact, we know the exact
direction of the optimal solution but we do not know from which point in the polytope we should start so that we directly reach the
optimal solution (corner).
While computing multiple zeros of a polynomial do
not pose any serious problem, the zero-clusters do pose serious a serious
(ill-conditioned) problem. Even ten zeros where each is successively greater
than the previous one by .01 could pose as an excellent test problem for any floating-point
algorithm with, say, 14 significant digit computation. In this context, an
error-free algorithm with parallel implementation was developed to get the
zero-clusters exactly (Engineering
Simulation,
·During
1970-85
To achieve stability/error-reduction, row/column
permutation is often resorted to in a matrix. While doing so, we may destroy
the structure of the matrix. For example, a sparse matrix having only a few
diagonals nonzero would loose its structure when row/column interchanges are
carried out. To obviate such a problem, we have developed a row/column
permutation-free rank-augmented algorithm triangularization
algorithm that obtains a generalized inverse of a matrix (IEEE Trans. Computers, Vol. C-23,
1974, pp. 199-201). Also developed are the optimal iterative schemes for
computing the minimum-norm least-squares inverse of a rectangular matrix; these
schemes are ever-convergent and produce the best possible inverse subject to
the precision of the computer (Int. J.
Systems Science, Vol. 8, 1976,
748-753. Also studied are the properties of rotated and reflected matrices (Matrix and Tensor Qrtly,
U.K., Vol. 22, 1971, pp. 60-65).
Different kinds of knots including knitting were
represented algorithmically as a line. One can read and mechanically follow the
characters in the line to achieve the desired knot. The representation is
concise and can be derived using the algorithm for almost all possible knots
involving one or two threads (
.
SYAMAL KUMAR SEN
RESUME: JAN 2008
Name: Syamal Kumar Sen
Designation: Professor, Computational
Mathematics/Science (including High-performance Algorithms, Modelling
and Simulation)
Current Affiliation: Department of Mathematical Sciences, Florida Institute of
Technology,
Age and Date of Birth: 65 years,
October 12, 1942.
Place of Birth: Basirhat, West Bengal,
e-mail: sksen@fit.edu
Office Address: Department of
Mathematical Sciences, Florida Institute of Technology,
Office Telephone: (321) 674-7714
Office Telefax:
(321) 674-7412
Residence Address:
Residence Telephone: (321) 956-8437
1. Details of Academic Qualification
(Degree Onwards)
Examination University/Institution Class Obtained Year
B.Sc. (PCM) Calcutta Hons. (Physics) 1961
Appl. Science Course Indian Statistical Institute, I 1965
On Computers
M.Sc. (Engg.) Indian Institute of Science, Research 1970
Ph. D. (Engg.) -do- Research 1973
1.1 Membership of Professional Bodies
Computer Society of India (Was also in the Editorial Board of the society’s journal Computer Science and Informatics)
Indian Society of Information Sciences
Indian Mathematical Society
Indian Society of Theoretical and Applied Mechanics (Life Member)
Instrument
Society of
Indian Institute of Science Alumni Association (Life Member)
Indian Society of Information Theory and Applications (ISITA)
Editorial
Board, Neural, Parallel & Scientific Computations,
1.2 Cited/Included
Dr.
Sen has been included/cited in Marquis Who’s Who (Sep 2005)
2. Details of Service
Current:
at Florida Institute of Technology,
Year
Designation
From To
2004 (Jan) to date Professor
______________________________________________________________________
At
the Indian Institute of Science (IISc),
Year
Designation
From To
1996(Mar) 2004 (Aug) Professor
1990(Mar) 1996(Mar) Associate Professor
1979 1990 Principal Research Scientist
1974 1979 Assistant Professor
1970 1974 Scientific Officer
1965 1970 Technical Assistant
Abroad (on leave from I.I.Sc.)
Rank/Title
University/Institution Date
Professor
Visiting Professor Florida Tech (USA) 1995-1996 (1 year)
Indo-US Fulbright Fellow
(as a senior teacher)
Associate Professor Al-Fateh
University,
Lecturer University of the West Indies, 1975-1976 (1 year)
Cave-Hill
3. Report of Work Done
3.1 Research and Scientific Investigation
3.1.1 Guidance of Students for Research Conferments
Supervised
several Ph.D., M.Sc. (Engg.),
M. Tech., and other masters degree students in
Recent (2006-2007) Ph.D. Dissertations Supervised by Me
- Random Number Generators: MC Integration and TSP-solving by Simulated Annealing, Genetic, and Ant System Approaches, Ph. D. Dissertation in Applied Mathematics, Tathagata Samanta, May 2006.
- Quasi-Versus Pseudo-random Numbers with Applications to Nonlinear Optimization, Ph.D. Dissertation in Operations Research, Andrea Noel Reese, December, 2006.
- Integration and Optimization: Irrational Numbers for Random Sequences and Scope of Evolutionary Algorithms, Ph.D. Dissertation in Operations Research, Gholam Ali Shaykhian, December 2007.
Recent
Masters Thesis Supervised by Me
1. Revisited Simulated Annealing: Experiment, Comparison and Parallelization on Large TSP, M.S. Thesis in Operations Research, Saswata Ghose, December 2005.
3.1.2
Guidance of
Students in Their Project Work
Also, supervised the projects of
several post-M.Sc./post B.E. programmer trainees,
M.E., M.S., B.E., and B.S. students in
3.1.3
Most Recent Sponsored Projects
(i) S.K. Sen, Principal
Investigator: IP Modeling for Optimal Growth of Thin Films: Sponsored by
Florida Solar Energy Center (FSEC), University of Central Florida, Cocoa,
Florida, July 01, 2006-June 30, 2007.
(ii) S.K. Sen, Principal Investigator: Efficiency of
Solar Cells: Making Modeling More Attractive to Experimentalists, Sponsored by
Florida Solar Energy Center (FSEC),
Books Published
1. Computer-based Numerical Algorithms (with E.V. Krishnamurthy), Affiliated East-West Press (affiliated to Van Nostrand), New Delhi, 437 + xxxiii pages, 18 cm ´ 24 cm, 1976 (published with a subsidy under the Indo-American Text-book programme operated by National Book Trust, India) mainly for graduate and research students.
2. Computer and Computing with Fortran 77 (with S.S. Alam), Oxford and IBH, New Delhi, 594 pages, 18 cm ´ 24 cm, 1988 ¾ an undergraduate text with over 65 Fortran 77 programs for science and engineering students. The second edition (subsidized by the Government of India through the National Book Trust, India for the benefit of the students) with an extensive revision and an addition of many new materials and examples was published in1996 [ Second Edition, 502 + xii pages, 18 cm ´ 24 cm, 1996].
3.
Computing
with BASIC: Problem Solving with Structure and Style (S.S. Alam), 219 pages, New Central Book
Agency,
4. 
Numerical
Algorithms: Computations in Science and Engineering (E.V.
Krishnamurthy), Affiliated East-West Press, New Delhi, 629 + xxii
pages, 18 cm ´ 24 cm, 1986 (subsidized by Government of India through National
Book Trust, India for the benefit of students) for mainly graduate and research
students. This book has been reprinted in 1989 and further reprinted with
the addition of significant materials on parallel computing several
modification and inclusions in 1993, in 1996, in 2000, and in 2001 (Used as a
text-book in Florida Tech, USA; also being used in several universities,
government institutes as well as laboratories in India and abroad as a
reference/textbook).
5. 
Programming in
MATLAB: With Examples from Krishnamurthy and Sen’