Beresford Parlett

Beresford Neill Parlett (born 1932) is an applied mathematician, specializing in numerical analysis and scientific computation.[2]

Beresford Parlett
Born (1932-07-04) July 4, 1932
London
NationalityUK
Alma materUniversity of Oxford (B.A.)
Stanford University (Ph.D.)
Scientific career
FieldsNumerical analysis
InstitutionsUniversity of California, Berkeley
ThesisI. Bundles of Matrices and the Linear Independence of Their Minors; II. Applications of Laguerre's Method to the Matrix Eigenvalue Problem[1] (1962)
Doctoral advisorGeorge Forsythe
Doctoral studentsInderjit Dhillon
Anne Greenbaum

Education and career

Parlett received in 1955 his bachelor's degree in mathematics from the University of Oxford and then worked in his father's timber business for three years. From 1958 to 1962 he was a graduate student in mathematics at Stanford University, where he received his Ph.D. in 1962. He was a postdoc for two years at Manhattan's Courant Institute and one year at the Stevens Institute of Technology. From 1965 until his retirement, he was a faculty member of the mathematics department at the University of California, Berkeley. There he served for some years as chair of the department of computer science, director of the Center for Pure and Applied Mathematics, and professor in the department of electrical engineering and computer science. He was a visiting professor at the University of Toronto, Pierre and Marie Curie University (Paris VI), and the University of Oxford.[3]

Parlett is the author of many influential papers on the numerical solution of eigenvalue problems, the QR algorithm, the Lanczos algorithm, symmetric indefinite systems, and sparse matrix computations.[3]

Awards and honours

Selected publications

Articles
  • Parlett, B. N.; Reinsch, C. (1969). "Balancing a matrix for calculation of eigenvalues and eigenvectors". Numerische Mathematik. 13 (4): 293–304. doi:10.1007/BF02165404.
  • Bunch, J. R.; Parlett, B. N. (1971). "Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations". SIAM Journal on Numerical Analysis. 8 (4): 639–655. Bibcode:1971SJNA....8..639B. doi:10.1137/0708060.
  • Parlett, B. N. (1974). "The Rayleigh quotient iteration and some generalizations for nonnormal matrices". Mathematics of Computation. 28 (127): 679. doi:10.1090/s0025-5718-1974-0405823-3.
  • Parlett, B. N.; Scott, D. S. (1979). "The Lanczos algorithm with selective orthogonalization". Mathematics of Computation. 33 (145): 217–238. doi:10.1090/s0025-5718-1979-0514820-3.
  • Kahan, W.; Parlett, B. N.; Jiang, E. (1982). "Residual Bounds on Approximate Eigensystems of Nonnormal Matrices". SIAM Journal on Numerical Analysis. 19 (3): 470–484. Bibcode:1982SJNA...19..470K. doi:10.1137/0719030.
  • Parlett, Beresford N.; Taylor, Derek R.; Liu, Zhishun A. (1985). "A look-ahead Lánczos algorithm for unsymmetric matrices". Mathematics of Computation. 44 (169): 105. doi:10.1090/s0025-5718-1985-0771034-2.
  • Nour-Omid, Bahram; Parlett, Beresford N.; Ericsson, Thomas; Jensen, Paul S. (1987). "How to implement the spectral transformation". Mathematics of Computation. 48 (178): 663. doi:10.1090/s0025-5718-1987-0878698-5.
  • Parlett, Beresford N. (1992). "Some basic information on information-based complexity theory". Bulletin of the American Mathematical Society. 26: 3–29. doi:10.1090/S0273-0979-1992-00239-2.[6]
  • Fernando, K. Vince; Parlett, Beresford N. (1994). "Accurate singular values and differential qd algorithms". Numerische Mathematik. 67 (2): 191–229. doi:10.1007/s002110050024.
  • Paige, Chris C.; Parlett, Beresford N.; Van Der Vorst, Henk A. (1995). "Approximate solutions and eigenvalue bounds from Krylov subspaces". Numerical Linear Algebra with Applications. 2 (2): 115–133. doi:10.1002/nla.1680020205.
  • Dhillon, Inderjit S.; Parlett, Beresford N. (2004). "Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices". Linear Algebra and Its Applications. 387: 1–28. doi:10.1016/j.laa.2003.12.028.
  • Bai, Zhong-Zhi; Parlett, Beresford N.; Wang, Zeng-Qi (2005). "On generalized successive overrelaxation methods for augmented linear systems". Numerische Mathematik. 102: 1–38. doi:10.1007/s00211-005-0643-0.
  • Shomron, Noam; Parlett, Beresford N. (2009). "Linear Algebra meets Lie Algebra: The Kostant–Wallach theory". Linear Algebra and Its Applications. 431 (10): 1745–1767. arXiv:0809.1204. doi:10.1016/j.laa.2009.06.007. ISSN 0024-3795. arXiv preprint (See Bertram Kostant and Nolan Wallach.)

Books
  • Parlett, Beresford N. (January 1998). The Symmetric Eigenvalue Problem. Philadelphia: SIAM. ISBN 9781611971163; SIAM corrected edition of the original publication by Prentice-Hall in 1980[7]
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References
  1. Beresford Neill Parlett at the Mathematics Genealogy Project
  2. "Beresford N. Parlett". Mathematics Department, U. C. Berkeley.
  3. Bunch, James R. (1995). "Editorial (introducing special issue dedicated to Beresford Parlett and William Kahan on their 60th birthdays)". Numerical Linear Algebra with Applications. 2 (2): 85. doi:10.1002/nla.1680020202. (See William Kahan.)
  4. "Prize History". SIAM Activity Group on LInear Algebra Best Paper Prize, SIAM.
  5. "Beresford N. Parlett". Electrical Engineering and Computer Sciences, U. C. Berkeley.
  6. Hirsch, Morris W.; Palais, Richard S. (1992). "Editors' remarks (on two complexity theory surveys in the Bulletin)". Bulletin of the American Mathematical Society. New Series. 26: 1–2. arXiv:math/9201262. doi:10.1090/S0273-0979-1992-00238-0.
  7. Stewart, G. W. (1981). "Book Review: The symmetric eigenvalue problem". Bulletin of the American Mathematical Society. 4 (3): 368–374. doi:10.1090/s0273-0979-1981-14918-1.
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