Robert E. Funderlic

Professor

Dr. Funderlic's main interests lie in the design, implementation and analysis of numerical linear algebra algorithms for high performance computing. His students often have close ties with the North Carolina Supercomputing Center with its IBM-SP and other advanced architectures. His interests span over most areas of numerical analysis and intersect with several diverse applications including most recently matrix factorizations applicable to data mining (current NSF Grant Abstract ), and atmospheric and environmental models ( related current (student) Andy Smith Ph.D. research ). [Dr. F. was department head from 1986 to 1992]

Representative Publications

"Optimizing Performance of Parallel Architectures Through Processor configuration and Data Distribution," (with C.D Wong, E.W. Davis and F. A. Smith) Journal of Parallel and Distributed Computing (under review).

"The Centroid Decomposition: Relationships Between Discrete Variational Decompositions and SVD," (with M. Chu) SIAM J. of Matrix Anal. Appl., 23(2002), 1025-1044.

"Structured low rank approximation," (with M. Chu and R. J. Plemmons), (to appear special issue of Linear Algebra and Its Appl.) Much of this appeared as "On nearest approximations of structured lower rank matrices" in Proceedings of SPIE, Advanced Signal Processing Algorithms, Architectures, and Implementations, VIII, Vol. 3461, F. Luk, ed., 268-279, (1998)

"Rank Modifications of Semi-definite Matrices with Applications to Secant Updates,"(with M. Chu and G. H. Golub) SIAM J. of Matrix Anal. Appl., 20(1998), 428-36.

"On a Variational Formulation of the Generalized Singular Value Decomposition," (with Moody Chu and Gene Golub), SIAM Journal on Matrix Anal. and Appli. 18(4): 1082-1092, (1997)

"A Rank-One Reduction Formula and Its Application to Matrix Factorizations," (with Moody Chu and Gene Golub), SIAM Review 37(4): 512-530, (1995)

"A Hypercube Implementation of the Implicit Double Shift QR Algorithm," (with G.A. Geist and G. Davis), Proceedings of the Second Conference on Hypercube Multiprocessors, pp. 619-626, SIAM Publications, M.T. Heath, editor, (1987)

"A Combined Direct-Iterative Method for Certain M-Matrix Linear Systems," (with R. J. Plemmons) SIAM Journal Algebraic and Discrete Methods 7, 30-42 (1986).

"Updating LU Factorizations for Computing Stationary Distributions," (with R.J. Plemmons), SIAM Journal Algebraic and Discrete Methods, 7, (1986), pp. 30-42.

"Sensitivity of the Stationary Distribution Vector for an Ergodic Markov Chain," (with C. D. Meyer, Jr.), Linear Algebra and its Applications, 78, (1986)

"Torus Data Flow for Parallel Computation of Missized Matrix Problems," (with George A. Geist), Linear Algebra and its Applications, No. 77, (1986) pp. 149 -163.

"LU Decompositions of Generalized Diagonal ly Dominant Matrices," (with R. J. Plemmons and M. Neumann) Numerische Mathematik, 44, 57-59 (1982).

"Solution of Homogeneous Systems of Equations from Compartmntal Models," (with J. B. Mankin) SIAM J. Sc. Stat. Comput. , 2, 375-83 (1981)

"LU Decomposition of M-matrices by Elimination Without Pivoting," (with R.J. Plemmons) Linear Algebra and Its Applications, 41, 99-110 (1981)

"The Rank of a Difference of Matrices and Associated Generalized Inverses," (with R. Cline) J. Linear Alg. Appl., 24 185-215 (1979).

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