Victor Pan

Victor Yakovlevich Pan (Russian: Пан Виктор Яковлевич) is a Soviet and American mathematician and computer scientist, known for his research on algorithms for polynomials and matrix multiplications, credited with coining the terms of active operations-basic substitution and trilinear aggregation. Google Scholar and DBLP show over 11,000 citations of his four books (1623 + LXXIV pages overall), over 20 surveys in journals and book chapters, over 180 research articles in journals, and over 100 in refereed conference proceedings such as STOC, FOCS, SODA, ICALP, SPAA, CSR, ISSAC, CASC, and SNC.

Education and career

Pan earned his Ph.D. at Moscow University in 1964, under the supervision of Anatoli Georgievich Vitushkin,[1] and continued his work at the Soviet Academy of Sciences. During that time, he published a number of significant papers and became known informally as "polynomial Pan" for his pioneering work in the area of polynomial computations. In late 1970s, he immigrated to the United States and held positions at several institutions including IBM Research. Since 1988, he has taught at Lehman College of the City University of New York.[2]

Contributions

Victor Pan is an expert in computational complexity and has developed a number of new algorithms. One of his notable early results is a proof that the number of multiplications in Horner's method is optimal.[CVP]

In the theory of matrix multiplication algorithms, Pan in 1978 published an algorithm with running time . This was the first improvement over the Strassen algorithm, and kicked off a long line of improvements in fast matrix multiplication that later included the Coppersmith–Winograd algorithm and subsequent developments.[SNO] He wrote the text How to Multiply Matrices Faster (Springer, 1984) surveying early developments in this area.[3][HMM] In 1998, with his student Xiaohan Huang, Pan showed that matrix multiplication algorithms can take advantage of rectangular matrices with unbalanced aspect ratios, multiplying them more quickly than the time bounds one would obtain using square matrix multiplication algorithms.[FRM]

Since that work, Pan has returned to symbolic and numeric computation and to an earlier theme of his research, computations with polynomials. He developed fast algorithms for the numerical computation of polynomial roots,[UP] and, with Bernard Mourrain, algorithms for multivariate polynomials based on their relations to structured matrices.[4][MPD] He also authored or co-authored several more books, on matrix and polynomial computation,[5][PMC] structured matrices,[6][SMP] and on numerical root-finding procedures.[7][NMR]

Recognition

Pan was appointed Distinguished Professor at Lehman College in 2000.[2]

In 2013 he became a fellow of the American Mathematical Society, for "contributions to the mathematical theory of computation".[8]

Selected publications

Research papers
CVP.Pan, V. Ja. (1966), "On means of calculating values of polynomials", Russian Math. Surveys, 21: 105–136, doi:10.1070/rm1966v021n01abeh004147, MR 0207178
SNO.Pan, V. Ya. (October 1978), "Strassen's algorithm is not optimal: Trilinear technique of aggregating, uniting and canceling for constructing fast algorithms for matrix operations", Proceedings of the 19th Annual Symposium on Foundations of Computer Science (FOCS 1978), IEEE, doi:10.1109/sfcs.1978.34, S2CID 14348408
FRM.Huang, Xiaohan; Pan, Victor Y. (1998), "Fast rectangular matrix multiplication and applications", Journal of Complexity, 14 (2): 257–299, doi:10.1006/jcom.1998.0476, MR 1629113
MPD.Mourrain, Bernard; Pan, Victor Y. (2000), "Multivariate polynomials, duality, and structured matrices" (PDF), Journal of Complexity, 16 (1): 110–180, doi:10.1006/jcom.1999.0530, MR 1762401 (winner, J. Complexity best paper award)[4]
UP.Pan, Victor Y. (2002), "Univariate polynomials: nearly optimal algorithms for numerical factorization and root-finding", Journal of Symbolic Computation, 33 (5): 701–733, doi:10.1006/jsco.2002.0531, MR 1919911

Books
HMM.Pan, Victor (1984), How to Multiply Matrices Faster, Lecture Notes in Computer Science, 179, Berlin: Springer-Verlag, doi:10.1007/3-540-13866-8, ISBN 3-540-13866-8, S2CID 5280107[3]
PMC.Bini, Dario; Pan, Victor Y. (1994), Polynomial and Matrix Computations, Vol. I: Fundamental Algorithms, Progress in Theoretical Computer Science, Boston, MA: Birkhäuser, doi:10.1007/978-1-4612-0265-3, ISBN 0-8176-3786-9, S2CID 30728536[5]
SMP.Pan, Victor Y. (2001), Structured Matrices and Polynomials: Unified Superfast Algorithms, New York: Springer-Verlag, doi:10.1007/978-1-4612-0129-8, ISBN 0-8176-4240-4[6]
NMR.McNamee, J. M.; Pan, V. Y. (2013), Numerical Methods for Roots of Polynomials, Part II, Studies in Computational Mathematics, 16, Amsterdam: Elsevier/Academic Press, ISBN 978-0-444-52730-1[7]

References
  1. Victor Pan at the Mathematics Genealogy Project
  2. Victor Pan of Lehman mathematics faculty selected as Distinguished Professor, Lehman College, archived from the original on 2018-02-14
  3. Reviews of How to Multiply Matrices Faster:
  4. "Best paper awards", Journal of Complexity, retrieved 2018-10-16
  5. Reviews of Polynomial and Matrix Computations:
  6. Review of Structured Matrices and Polynomials:
  7. Review of Numerical Methods for Roots of Polynomials, Part II:
    • Proinov, Petko D., Mathematical Reviews, MR 3293902CS1 maint: untitled periodical (link)
  8. "List of Fellows of the American Mathematical Society", American Mathematical Society, retrieved 22 May 2015
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