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Office Location

Stratton Hall 009A

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Education:

BA Rice University 1966

MS New York University 1968

PhD New York University 1970

Office Location

Stratton Hall 009A

Contact

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

Scholarly Work:

On the null-spaces of elliptic partial differential operators in Rn

A Fredholm theory for elliptic partial differential operators in Rn - 1971

The null-spaces of elliptic partial differential operators in Rn - 1972

On the estimation of the L2-norm of a function over a bounded subset of Rn - 1972

On minimizing the probability of misclassification for linear feature selection - 1973

On minimizing the probability of misclassification for linear feature selection - 1973

Well-posedness of certain elliptic problems in unbounded domains - 1973

On the null-spaces of partially elliptic operators of a certain type - 1975

Some remarks on the local energy decay of solutions of the initial-boundary value problem for the wave equation in unbounded domains - 1975

Strong ellipticity and Van Hove's lemma in inhomogeneous media - 1975

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions - 1976

The numerical evaluation of the maximum-likelihood estimate of a subset of mixture proportions - 1977

Estimating the proportions of two populations in a mixture using linear maps - 1977

Convergence theorems for least-change secant update methods - 1978

Mixture densities, maximum likelihood, and the EM algorithm - 1978

Inaccuracy in quasi-Newton methods: local improvement theorems - 1980

Experiments with quasi-Newton methods for solving stiff ODE systems - 1981

Least-change sparse secant update methods with inaccurate secant conditions - 1984

Implementation of GMRES method using Householder transformations - 1984

Asymptotics of solute dispersion in periodic porous media - 1985

Newton-like methods for underdetermined systems - 1985

Least-change secant update methods for underdetermined systems - 1988

Least-change secant updates of nonsquare matrices - 1989

Experiments with conjugate algorithms for homotopy curve tracking - 1990

Preconditioned iterative methods for homotopy cure tracking - 1990

Efficient high accuracy solutions with GMRES(m) - 1990

Residual smoothening techniques for iterative methods - 1991

Globally convergent inexact Newton methods - 1992

A simpler GMRES - 1992

Residual smoothing and peak/plateau behavior in Krylov subspace methods - 1994

Choosing the forcing terms in an inexact Newton method - 1994

GMRES on (nearly) singular systems - 1994

An approach to continuation using Krylov subspace methods - 1995

An inexact Newton method for fully-coupled solution of the Navier-Stokes equations with heat and mass transport - 1996

Algorithm 777: HOMPACK90: a suite of FORTRAN 90 codes for globally convergent homotopy algorithms - 1997

NITSOL: a Newton iterative solver for nonlinear systems - 1997

A new adaptive GMRES algorithm for achieving high accuracy - 1997

An adaptation of Krylov subspace methods to path following problems - 1997

A 3-D model with fluid-structure interactions for unsteady blood flow in stenotic arteries with cyclic wall collapse - 1998

Simulating cyclic artery compression using a 3-D unsteady model with fluid-structure interactions - 1998

On backtracking failure in Newton-GMRES methods with a demonstration for the Navier-Stokes equations - 2000

A Fredholm theory for a class of first-order elliptic operators in Rn - 2000

On the null-spaces of first-order elliptic operators in Rn - 2001

2D and 3D multi-physics models for flow and nonlinear stress/strain analysis of stenotic arteries with lipid cores - 2001

An iterative method for symmetric indefinite linear systems - 2002

Globalization techniques for Newton-Krylov methods and applications to the fully-coupled solution of the Navier-Stokes equations - 2002

On using approximate finite-differences in matrix-free Newton-Krylov methods - 2003

Inexact Newton dogleg methods - 2004

Anderson acceleration for fixed-point iterations - 2006

An accelerated Picard method for nonlinear systems related to variably saturated flow - 2008

Solution methods for large-scale nonlinear problems: an evolving research area - 2008

Workshop on solution methods for large-scale nonlinear problems - 2011

Professional Highlights & Honors:

First Governor's Medal for Science and Technology

1987

State of Utah

College of Science Researcher of the Year

1994

Utah State University

ISI Highly Cited Researcher in Mathematics

2003

WPI Board of Trustees Award for Outstanding Research and Creative Scholarship

2005