William B. Gragg

William B. Gragg
Born November 2, 1936 (1936-11-02) (age 80)
Bakersfield, California
Nationality American
Fields Mathematics
Institutions Naval Postgraduate School
Alma mater UCLA
Thesis Repeated extrapolation to the limit in the numerical solution of ordinary differential equations (1964)
Doctoral advisor Peter Henrici
Known for Gragg Extrapolation

William B. Gragg is Emeritus Professor in the Department of Applied Mathematics at the Naval Postgraduate School. He has made fundamental contributions in numerical analysis, particularly the areas of numerical linear algebra and numerical methods for ordinary differential equations.

He received his PhD at UCLA in 1964 under the direction of Peter Henrici. His dissertation work resulted in the Gragg Extrapolation method[1] for the numerical solution of ordinary differential equations (sometimes also called the Bulirsch–Stoer algorithm).

Gragg is also well known for his work on the QR algorithm for unitary Hessenberg matrices, on updating the QR factorization,[2] superfast solution of Toeplitz systems,[3] parallel algorithms for solving eigenvalue problems,[4][5] as well as his exposition on the Pade table and its relation to a great number of algorithms in numerical analysis.[6]

References

  1. ↑ http://epubs.siam.org/doi/pdf/10.1137/0702030 On extrapolation algorithms for ordinary initial value problems, WB Gragg SINUM, vol. 2, no. 3, 1965.
  2. ↑ Daniel, J. W.; Gragg, W. B.; Kaufman, L.; Stewart, G. W. (1976). "Reorthogonalization and stable algorithms for updating the Gram-Schmidt factorization". Math. Comp. 30: 772–795. doi:10.1090/S0025-5718-1976-0431641-8.
  3. ↑ "Superfast Solution of Real Positive Definite Toeplitz Systems". SIAM Journal on Matrix Analysis and Applications. 9: 61–76. doi:10.1137/0609005.
  4. ↑ http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA262297 A Parallel Divide and Conquer Algorithm for the Generalized Real Symmetric Definite Tridiagonal Eigenproblem, C.F. Borges and W.B.Gragg, 1992
  5. ↑ "A divide and conquer method for unitary and orthogonal eigenproblems". Numerische Mathematik. 57: 695–718. doi:10.1007/BF01386438.
  6. ↑ "The Padé Table and Its Relation to Certain Algorithms of Numerical Analysis". SIAM Review. 14: 1–62. doi:10.1137/1014001.
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