Homer F. Walker, Professor Emeritus
Mathematical Sciences Department
Worcester Polytechnic Institute

Contact Information

Email
 walker<at>wpi<dot>edu
Mailing Address
 486 Riverview Drive
Chatham, MA 02633




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SIAM LA21 talk slides:  Anderson Acceleration: An Overview


Course Materials
Current 
 No current courses
Previous 
Undergraduate
MA 1022: Calculus II - Integral Calculus, B Term 2006
MA 1023: Calculus III, C Term 2009
MA 1024: Calculus IV, D Term 2010
MA 2073: Matrices and Linear Algebra II, C Term 2010
MA 3257/CS 4032:  Numerical Methods for Linear and Nonlinear Systems, C Term 2013
MA 3457/CS 4033: Numerical Methods for Calculus and Differential Equations, B Term 2009
MA 4291: Applicable Complex Variables, C Term 2012
Graduate
MA 500: Basic Real Analysis, Fall 2013
MA 510/CS 522: Numerical Methods, Fall 2005
MA 512: Numerical Differential Equations, Spring 2017
MA 514: Numerical Linear Algebra, Spring 2018
MA 590 (Special Topics): Numerical Methods for Nonlinear Equations and
                                         Unconstrained Optimization, Fall 2009
MA 590 (Special Topics): Applied Linear Algebra, Fall 2013
Curriculum Vitae (PDF) with a complete list of publications.

Software:  NITSOL, a Fortran code for Newton-iterative solution of large-scale nonlinear systems.

Downloadable papers
Accelerating the Uzawa algorithm, with N. Ho and S. D. Olson, SIAM J. Sci. Comput., 39 (2017), S461-S476.

An accelerated fixed-point iteration for solution of variably saturated flow, with C. S. Woodward and U. M. Yang, Proceedings of the XVIII International Conference on Water Resources, CMWR~2010, J. Carrera, ed., CIMNE, Barcelona, 2010 (available online at http://congress.cimne.com/CMWR2010/Proceedings/Start.html). 

Anderson acceleration for fixed-point iterations, with P. Ni, SIAM J. Numer. Anal., 49 (2011), 1715-1735.
 
Inexact Newton dogleg methods, with R. P. Pawlowski, J. P. Simonis, and J. N. Shadid, SIAM J. Numer. Anal., 46 (2008), 2112-2132.

On using approximate finite-differences in matrix-free Newton-Krylov methods, with P. N. Brown, R. Wasyk, and C. S. Woodward, SIAM J. Numer. Anal., 46 (2008), 1892-1911.

Globalization techniques for Newton-Krylov methods and applications to the fully-coupled solution of the Navier-Stokes equations, with R. P. Pawlowski, J. N. Shadid, and J. P. Simonis, SIAM Review, 48 (2006), 700-721.

Globalization techniques for Newton-Krylov methods and applications to the fully-coupled solution of the Navier-Stokes equations, with R. P. Pawlowski, J. N. Shadid, and J. P. Simonis, Report SAND2004-1777, Sandia National Laboratories, May, 2004.

On backtracking failure in Newton-GMRES methods with a demonstration for the Navier-Stokes equations, with R. S. Tuminaro and J. N. Shadid, J. Comp. Physics, 180 (2002), 549-558.

Simulating cyclic artery compression using a 3-D unsteady model with fluid-structure interactions, with D. Tang, C. Yang, S. Kobayashi, and D. N. Ku, Computers and Structures, 80 (2002), 1651-1665.

An adaptation of Krylov subspace methods to path following problems, SIAM J. Sci. Comput., 21 (2000), pp. 1191-1198.

NITSOL: a Newton iterative solver for nonlinear systems, with M. Pernice, Special Issue on Iterative Methods, SIAM J. Sci. Comput., 19 (1998), 302-318.

A new adaptive GMRES algorithm for achieving high accuracy, with M. Sosonkina, L. T. Watson, R. K. Kapania, Numer. Linear Algebra Appl., 5(1998), 275-297.

GMRES on (nearly) singular systems, with P. N. Brown, SIAM J. Matrix Anal. Appl., 18 (1997), 37-51.

An inexact Newton method for fully-coupled solution of the Navier-Stokes equations with heat and mass transfer, with J. N. Shadid and R. S. Tuminaro, J. Comp. Physics, 137 (1997), 155-185.

Algorithm 777: HOMPACK90: a suite of Fortran 90 codes for globally convergent homotopy algorithms, with L. T. Watson, M. Sosonkina, R. C. Melville, and A. P. Morgan, ACM Trans. Math. Software, 23 (1997), 514-549.

Choosing the forcing terms in an inexact Newton method, with S. C. Eisenstat, Special Issue on Iterative Methods in Numerical Linear Algebra, SIAM J. Sci. Comput., 17 (1996), 16-32.

Residual smoothing and peak/plateau behavior in Krylov subspace methods, Appl. Numer. Math., 19 (1995), 279-286.

A simpler GMRES, with L. Zhou, Numer. Linear Algebra Appl., 1 (1994), 571-581.

Globally convergent inexact Newton methods, with S. C. Eisenstat, SIAM J. Optimization, 4 (1994), pp. 393-422.

Residual smoothing techniques for iterative methods, with L. Zhou, Special Section on Iterative Methods in Numerical Linear Algebra, SIAM J. Sci. Comput., 15 (1994), pp. 297-312.

Efficient high accuracy solutions with GMRES(m), with K. Turner, SIAM J. Sci. Stat. Comput., 13 (1992), pp. 815-825.

Preconditioned iterative methods for homotopy curve tracking, with C. Desa, K. M. Irani, C. J. Ribbens, and L. T. Watson, Special Issue on Iterative Methods in Numerical Linear Algebra, SIAM J. Sci. Stat. Comput., 13 (1992), pp. 30-46.

Experiments with conjugate gradient algorithms for homotopy curve tracking, with K. M. Irani, M. P. Kamat, C. J. Ribbens, and L. T. Watson, SIAM J. Optimization, 1 (1991), pp. 222-251.

Least-change secant updates of nonsquare matrices, with S. K. Bourji, SIAM J. Numer. Anal., 27 (1990), pp. 1263-1294.

Least-change secant update methods for underdetermined systems, with L. T. Watson, SIAM J. Numer. Anal., 27 (1990), pp. 1227-1262.

Asymptotics of solute dispersion in periodic porous media, with R. Bhattacharya and V. K. Gupta, SIAM J. Appl. Math., 49 (1989), pp. 86-98.

Implementation of the GMRES method using Householder transformations, SIAM J. Sci. Stat. Comput., 9 (1988), pp. 152-163.

Least-change sparse secant update methods with inaccurate secant conditions, with J. E. Dennis, Jr., SIAM J. Numer. Anal., 22 (1985), pp. 760-778.

Experiments with quasi-Newton methods for solving stiff ODE systems, with P. N. Brown and A. C. Hindmarsh, SIAM J. Sci. Stat. Comput., 6 (1985), 297-313.

Mixture densities, maximum likelihood, and the EM algorithm, with R. A. Redner, SIAM Review, 26 (1984), 195-239.

Convergence theorems for least-change secant update methods, with J. E. Dennis, Jr., SIAM J. Numer. Anal., 18 (1981), pp. 949-987.

The numerical evaluation of the maximum-likelihood estimate of a subset of mixture proportions, with B. C. Peters, Jr., SIAM J. Appl. Math., 35 (1978), pp. 447-552.

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, with B. C. Peters, Jr., SIAM J. Appl. Math., 35 (1978), pp. 362-378.

Some remarks on the local energy decay of solutions of the initial-boundary value problem for the wave equation in unbounded domains, J. Diff. Equations, 23 (1977), 459-471.

On the null-spaces of partially elliptic operators of a certain type, with J. A. LaVita, J. Math. Anal. Appl., 55 (1976), 375-379.

On minimizing the probability of misclassification for linear feature selection, with L. F. Guseman, Jr., and B. C. Peters, Ann. Stat., 3 (1975), 661-668.

The null spaces of elliptic partial differential operators in R^n, with L. Nirenberg, J. Math. Anal. Appl., 42 (1973), 271-301.

On the estimation of the L_2-norm of a function over a bounded subset of R^n, Proc. Amer. Math. Soc., 38 (1973), 103-110.

On the null-spaces of elliptic partial differential operators in R^n, Trans. Amer. Math. Soc., 173 (1972), 263-275.

A Fredholm theory for a class of first-order elliptic partial differential operations in R^n, Trans. Amer. Math. Soc., 165 (1972), 75-86.

On the null-spaces of first-order elliptic partial differential operators in R^n, Proc. Amer. Math. Soc., 30 (1971), 278-286.