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Contact Information

Office:
Stratton Hall, 009A
Phone: +1-508-831-6113
Fax: +1-508-831-5824
walker@wpi.edu

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Homer F. Walker

Homer Walker's research and teaching interests are generally in computational and applied mathematics. In recent years, his research has been mainly concerned with developing and analyzing numerical algorithms for solving systems of linear and nonlinear equations, especially the very large systems that arise in modeling complex physical phenomena such as fluid flow. Previous research interests include numerical methods for unconstrained optimization, differential equations, and statistical estimation. When possible, he likes to work with experts in other areas of science and engineering to explore the practical effectiveness of the algorithms that he studies. Much of his work has been done in collaboration with researchers at U.S. national laboratories who have extensive experience with both challenging applications and advanced hardware and software for high-performance computing.

Walker enjoys bringing insights gained through his research to his teaching. This is especially important in computational mathematics courses because of the very dynamic nature of the area. These courses typically attract students from many departments in addition to Mathematical Sciences, reflecting not only the importance of the subject to modern science and engineering, but also the ease of pursuing interdisciplinary study at WPI.

Research Interests

  • Computational mathematics
  • Numerical methods for systems of linear and nonlinear equations
  • Numerical methods for unconstrained optimization, differential equations, and statistical estimation
  • Large-scale and high-performance computing

Education

  • BA, Rice University, 1966
  • MS, New York University, 1968
  • PhD, New York University, 1970

Featured Publications

  • P. A. Lott, H. F. Walker, C. S. Woodward, and U. M. Yang, "An accelerated Picard method for nonlinear systems related to variably saturated flow," Advances in Water Resources, 38 (2012), 92-101.
  • H. F. Walker and P. Ni, "Anderson acceleration for fixed-point iterations," SIAM J. Numer. Anal., 49 (2011), 1715-1735.
  • R. P. Pawlowski, J. P. Simonis, H. F. Walker, and J. N. Shadid, "Inexact Newton dogleg methods," SIAM J. Numer. Anal., 46 (2008), 2112-2132.
  • P. N. Brown, H. F. Walker, R. Wasyk, and C. S. Woodward, "On using approximate finite-differences in matrix-free Newton-Krylov methods," SIAM J. Numer. Anal., 46 (2008), 1892-1911.
  • R. P. Pawlowski, J. N. Shadid, J. P. Simonis, H. F. Walker, "Globalization techniques for Newton-Krylov methods and applications to the fully-coupled solution of the Navier-Stokes equations," SIAM Review, 48 (2006), 700-721.

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Professional Highlights

  • WPI Board of Trustees Award for Outstanding Research and Creative Scholarship (2005)
  • ISI Highly Cited Researcher in Mathematics (since 2003)
  • College of Science Researcher of the Year, Utah State University (1994)
  • First Governor's Medal for Science and Technology, State of Utah (1987)
 
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