vpanlehman.cuny.edu

Distinguished Professor

Department of Mathematics and Computer Science, at Lehman College of the City University of New York and the Cuny Graduate Center Ph.D. Program in Computer Science.

Internationally recognized leader in the field of computer science research.

· Algebraic Computation

· Numerical Computation

· Design and Analysis of Algorithms

· Computations with Dense Structured Matrices

In his research, Dr. Pan focuses on numerical and algebraic algorithms, which are the backbone of present-day computations in the sciences, engineering and communications. One of his major efforts involves devising effective new computational methods that combine the techniques of faster numerical computations with bounded precision and slower algebraic techniques for error-free symbolic computing. He has been responsible for several major breakthroughs, including new algorithms that greatly shortened the time needed to perform some fundamental computer computations.

Membership in Professional Societies:

· American Math. Society

· Society for Industrial and Applied Math.

· Association for Computing Machinery

· European Association for Theoretical Computer Science

Research Monographs

Polynomial and Matrix Computations, Volume 2: Selected Topics (with D. Bini), Birkhaeuser, Boston (2004) to appear.

Structured Matrices and Polynomials: Unified Superfast Algorithms, Birkhaeuse/Springer, Boston/New York (2001).

Polynomial and Matrix Computations, Volume 1: Fundamental Algorithms (XVI + 415 pages) (with D. Bini), in the series Progress in Theoretical Computer Science (R.V. Book editor), Birkhaeuser, Boston (1994).

How to Multiply Matrices Faster, Lecture Notes in Computer Science, vol. 179 (212 pages), Springer Verlag, Berlin (1984).

Chapters in Books and Survey Articles (items 1, 3, 4, 5, 8 present new research results)

"Fast Fourier Transform and Its Applications" (with I. Z. Emiris), Chapter 18 in Handbook "Algorithms and Theory of Computations", ch. 17, pp. 17-1 to 17-30, M. Atallah, editor, CRC Press Inc., Boca Raton, Florida (1999).

"Algebraic Algorithms" (with A. Diaz, I. Z. Emiris, and E. Kaltofen), Chapter 17 in Handbook "Algorithms and Theory of Computations", ch. 16, pp. 16-1 to 16-27, M. Atallah, editor, CRC Press Inc., Boca Raton (1999).

"Some Recent Algebraic/Numerical Algorithms", Electronic Proceedings of IMACS/ACA ‘98.

"Computational Complexity of Solving Large Sparse and Large Special Linear Systems of Equations", pp. 1-24, in "Algorithms for Large Scale Linear Algebraic Systems: Applications in Science and Engineering", G. Winter Althaus and E. Spedicato editors, NATO Advanced Science Institute Series, Kluwer Academic Publishers , Dordrecht, The Netherlands

"Solving Polynomials with Computers", American Scientist, 86, 62-69, (January-February 1998).

"Solving a Polynomial Equation: Some History and Recent Progress", SIAM Review, 39, 2, 187-220 (1997).

"Algebraic Algorithms" (with A. Diaz and E. Kaltofen), Chapter 10 in The Computer Science and Engineering Handbook, Alllen B. Tucker, Jr., (editor), 226-249, CRC Press Inc., Boca Raton, Florida (1997).

"Parallel Solution of Sparse Linear and Path Systems", in Synthesis of Parallel Algorithms (J.H. Reif editor), Chapter 14, pp. 621-678. Morgan Kaufmann publishers, San Mateo, California (1993).

"Complexity of Computations with Matrices and Polynomials," SIAM Review, 34, 2, 225-262 (1992).

"Complexity of Algorithms for Linear Systems of Equations", in Computer Algorithms for Solving Linear Algebraic Equations (The State of the Art), edited by E. Spedicato, NATO ASI Series, Series F: Computer and Systems Sciences, 77, 27-56, Springer, Berlin (1991) and Academic Press (1992).

"Linear Systems of Algebraic Equations", in Encyclopedia of Physical Sciences and Technology, 7, 304-329 (1987), (first edition, Marvin Yelles, editor); 8, 779-804 (1992) (second edition); and 8, (2001) (third edition, Robert A. Meyers, editor); Academic Press, San Diego, California.

“How Can We Speed Up Matrix Multiplication?", SIAM Review, 26, 3, 393-415 (1984).

On Methods of Computing the Values of Polynomials", Uspekhi Matematicheskikh Nauk, 21,1 (127), 103-134 (1966).(Transl. Russian Mathematical Surveys, 21,1 (127), 105-137 (1966).)

Research Articles (in journals and refereed proceedings of conferences)

"Toeplitz and Hankel Meet Hensel and Newton Modulo a Power of Two" (by V. Y. Pan, B. Murphy, R. E. Rosholt and X. Wang), preprint (2005).

"A Homotopic/Factorization Process for Toeplitz-like Matrices with Newton’s/Conjugate Gradient Stages", preprint (2005).

“Homotopic Residual Correction Algorithms for General and Structures Matrices" (by V.Y. Pan, M. Kunin, R. Rosholt, and H. Kodal), Math. of Computation, in press.

“The Amended DSeSC Power Method for Polynomial Root-finding”, Computers and Mathematics with Applications, in press.

“Coefficient-free Adaptation of Polynomial Root-finders”, Computers and Mathematics with Applications, in press.

"The Perturbation/Realization Approach to the Matrix Eigenproblem" (by V. Y. Pan, B. Murphy, R. E. Rosholt, X. Wang), Computers and Mathematics with Applications, in press.

"Fast and Stable QR Eigenvalue Algorithms for Generalized Semiseparable Matrices and Secular Equations" (by D.A. Bini, L. Gemignani and V.Y. Pan), Numerische Mathematik, in press.

"Can the TPR1 Structure Help Us to Solve the Algebraic Eigenproblem?”, in Proc. of the 16th Ann. ACM-SIAM Symposium on Discrete Algorith (SODA ‘05), 1069-1078, ACM Press, New York, and SIAM Publications, Philadelphia (January 2005).

“Improved Algorithms for Computing Determinants and Resultants" (by I. Z. Emiris and V. Y. Pan), J. of Complexity, 21, 1, 43-71 (2005).

“An Efficient Solution for Cauchy-like Systems of Linear Equations” (by Z. Chen and V. Y. Pan), Computers and Mathematics with Applications, 48, 529-537 (2004).

“On Theoretical and Practical Acceleration of Randomized Computation of the Determinant of an Integer Matrix” , Zapiski Nauchnykh Seminarov POMI (in English), Vol. 316, St. Petersburg, Russia (2004).

"Improved Initialization of the Accelerated and Robust QR-like Polynomial Root-finding" (by D. A. Bini, L. Gemignani, and V. Y. Pan), Electronic Transactions on Numerical Analysis, 17, 195-205 (2004). (Proc. version in Proceedings of the 7th International Workshop on Computer Algebra in Scientific Computing (CASC ‘04), St. Petersburg, Russia (July 2004), (edited by E. W. Mayr, V. G. Ganzha, E. V. Vorozhtzov), 39-50, Technische Univ. München, Germany (2004).) Proceedings Version

“Newton-like Iteration Based on Cubic Polynomials for Structured Matrices” (by G. Codevico, V. Y. Pan, and M. Van Barel), Numerical Algorithms, 36, 365-380 (2004).

"The Least-Squares Compression Policy for Newton-like Iteration for Structured Matrices" (by G. Codevico, V.Y. Pan, M. Van Barel, X. Wang, and A.-L. Zheng) in Proceedings of the 6th International Mathematica Symposium (IMS 2004) (edited by C. Jacob and P. Mitic), Banff, Alberta, Canada (August 2004).

"Iterative Inversion of Structured Matrices" (by V. Y. Pan, M. Van Barel, X. Wang and G. Codevico), Theoretical Computer Science, 315, 2-3, 581-592 (2004).

"On Rational Number Reconstruction and Approximation" (by V. Y. Pan and X. Wang), SIAM J. on Computing, 33, 2, 502-503 (2004).

"Inverse Power and Durand-Kerner Iteration for Univariate Polynomial Root-Finding "(by D.A. Bini, L. Gemignami and V.Y. Pan), Computers and Mathematics (with Applications), 2003.

"Improved Computation of Determinants and Resultants" (by I.Z. Emiris and V.Y. Pan), Proc. of the 6th International Workshop on Computer Algebra in Scientific Computing (CASC '03), (E.W. Mayr, V.G. Ganzha, E.V. Vorozhtzov, Editors), 81-94, Technische Univ. Muenchen, Germany, 2003.

"Acceleration of Euclidean Algorithm and Rational Number Reconstruction", (by X. Wang and V. Y. Pan), SIAM J. of Computing, 32, 2, 548-556 (2003).

"Matrix Structure and Loss-Resilient Encoding/Decoding", Computers & Mathematics (with Applications), 46, 493-499 (2003).

"Inversion of Displacement Operators", (by V.Y. Pan and X. Wang), SIAM J. on Matrix Analysis and Applications, 24, 3, 660-677 (2003).

"Accelerated Solution of Multivariate Polynomial Systems of Equations", (by B. Mourrain, V.Y. Pan, and O. Ruatta), SIAM J. on Computing, 32, 2, 435-454 (2003).

"Can We Optimize Toeplitz/Hankel Computations? ", Proc. of the 5th International Workshop on Computer Algebra in Scientific Computing (CASC ‘02), ( E. W. Mayr, V. G. Ganzha, E. V. Vorozhtzov, Editors), 253-264, Technische Univ. Muenchen, Germany (2002).

"Univariate Polynomials: Nearly Optimal Algorithms for Numerical Factorization and Root-Finding", J. of Symbolic Computation, 33, 5, 701-733 (2002)

"Acceleration of Euclidean Algorithm and Extensions", (by V.Y. Pan and X. Wang), Proc. International Symp. on Symbolic and Algebraic Computation, (ISSAC ‘02), 207-213, ACM Press, New York (2002).

"Symbolic and Numerical Methods for Exploiting Structure in Constructing Resultant Matrices", (by I. Z. Emiris and V.Y. Pan), Journal of Symbolic Computation, 33, 393-413 (2002).

"Randomized Acceleration of Fundamental Matrix Computations", Proc. of Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, 215-226, Springer, Berlin (2002).

"Structured Matrices and Newton’s Iteration: Unified Approach", (by V.Y. Pan, Y. Rami and X. Wang), Linear Algebra and Its Applications, 343/344, 233-265 (2002).

"Nearly Optimal Algorithms for Numerical Univariate Polynomial Factorization and Rootfinding I: Splitting a Polynomial into Factors over an Annulus", Proceedings of the Smalefest 2000, F. Cucker and M. Rojas (Eds.), Foundations of Computational Math. Series, 325-353, World Scientific, New Jersey (2002).

"Asymptotic Acceleration of the Solution of Multivariate Polynomial Systems of Equations", (by B. Mourrain, V.Y. Pan and O. Ruatta), Proceedings of the Smalefest 2000, F. Cucker and M. Rojas (Eds.), Foundations of Computational Math. Series, 267-294, World Scientific, New Jersey (2002).

“Univariate Polynomials: Nearly Optimal Algorithms for Factorization and Rootfinding”, Proc. International Symp. on Symbolic and Algebraic Computation, (ISSAC '01) 253-267, ACM Press, New York (July 2001).

"Numerical Computation of a Polynomial GCD and Extensions", Information and Computation, 167, 2, 71-85 (2001). (Only draft available)

“Parallel Matrix Multiplication on a Linear Array with a Reconfigurable Pipelined Bus System”, (with Keqin Li), IEEE Transactions on Computing, 50, 5, 519-525, (2001).

"Certification of Numerical Computation of the Sign of the Determinant of a Matrix" (with Y. Yu), Algorithmica, 30, 708-724, (2001).

“Newton’s Iteration for the Inversion of Structured Matrices” (with Y. Rami), in “Structured Matrices: Recent Developments in Theory and Computation”, 79-90, edited by D. Bini, E. Tyrtyshnikov and P. Yalamov, Nova Science Publishers, USA (2001).

“A Homotopic Residual Correction Process”, Proc. of the Second Conference on Numerical Analysis and Applications (L. Vulkov, J. Wasniewsky and P. Yalamov, editors), Lecture Notes in Computer Science, 1988, 644-649, Springer, Berlin (2001).

“A New Proximity Test for Polynomial Zeros”, Computers & Math. (with Applications), 41, 12, 1559-1560 (2001).

“Computation of a Specified Root of a Polynomial System of Equations Using Eigenvectors" (with D. Bondyfalat and B. Mourrain), Linear Algebra and Its Applications, 319, 193-209 (2000).

“Parallel Complexity of Computations with General and Toeplitz-like Matrices Filled with Integers”, SIAM J. on Computing, 30, 1080-1125 (2000).

“Matrix Structure, Polynomial Arithmetic, and Erasure-Resilient Encoding/Decoding”, Proc. Intern. Symp. on Symbolic and Algebraic Computations (ISSAC ‘2000), 266-271, ACM Press, New York (2000).

“Superfast Algorithms for Cauchy-like Matrix Computations and Extensions” (with A. Zheng), Linear Algebra and Its Applications, 310, 83-108 (2000).

“New Techniques for the Computation of Linear Recurrence Coefficients”, Finite Fields and Their Applications, 6, 93-118 (2000).

"Lifting/Descending Processes for Polynomial Zeros and Applications" (with B. Mourrain), J. of Complexity, 16, 1, 265-273 (2000).

"Multivariate Polynomials, Duality and Structured Matrices" (with B. Mourrain), J. of Complexity, 16, 1, 110-180 (2000).

"Approximating Complex Polynomial Zeros: Modified Quadtree (Weyl's) Construction and Improved Newton's Iteration", J. of Complexity, 16, 1, 213-264 (2000).

“Nearly Optimal Computations with Structured Matrices”, Proc. of 11th Ann. ACM-SIAM Symposium on Discrete Algorithms, 953-962, ACM Press, New York, and SIAM Publications, Philadelphia (January 2000).

Reports and Manuscripts

“Inversion of Displacement Operators”, (with X. Wang), Preliminary Report, (2001).

“A Unified Superfast Divide-and-Conquer Algorithm for Structured Matrices”, MSRI Preprint 1999-033, Mathematical Sciences Research Institute, Berkeley, California (1999).

“Computations with Structured Matrices”, (with B. Murphy and R. Rosholt), MSRI Preprint 1999-021, Mathematical Sciences Research Institute, Berkeley, California (1999).

"New Deterministic Parallel Algorithms for the Characteristic Polynomial of a Matrix over Abstract Fields", MSRI Preprint 1999-011, Mathematical Sciences Research Institute, Berkeley, California (1999).

"The Complexity of the Algebraic Eigenproblem" (with Z. Chen and A. Zheng), MSRI Preprint 1998-71, Mathematical Sciences Research Institute, Berkeley, California (1998).

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