



Anderson, Donald
Harvard University
Cambridge, Massachusetts








Date Reviewed 


1  10 of 32
reviews








Uniform pointwise convergence of finite difference schemes using grid equidistribution Linß T. Computing 66(1): 2739, 2001. Type: Article The issue addressed in this paper is resolving the boundary layer in a model convectiondiffusion ordinary differential equation boundary value problem involving a small parameter . The finite difference discretization procedure uses a nonuni...

Jun 1 2001 






On stopping criteria in verified nonlinear systems or optimization algorithms Kearfott R., Walster G. ACM Transactions on Mathematical Software 26(3): 373389, 2000. Type: Article The basic tool in the verified solution of constrained or unconstrained optimization or rootfinding problems is the interval Newton method. Analogues of conventional termination criteria can be problematic, potentially leading to inadequate answe...

Dec 1 2000 






Algorithm 801: POLSYS_PLP: a partitioned linear product homotopy code for solving polynomial systems of equations Wise S., Sommese A., Watson L. ACM Transactions on Mathematical Software 26(1): 176200, 2000. Type: Article The problem of solving large systems of polynomial equations arises in many application areas and poses difficult mathematical questions and computational challenges. This paper critically reviews the literature of the past two decades, during whi...

Jun 1 2000 






A multiplicity result for a periodic boundary value problem Rudolf B. Nonlinear Analysis: Theory, Methods & Applications 28(1): 137144, 1997. Type: Article The problem considered is of the form x″ ( t ) + f ( x ( t ) ) sgn ( x ( t ) ) x( t ) ^{m} + g ( t, x( t ) ) = s( t ), for 0 <...

Aug 1 1998 






On the rate of convergence of 2term recursions in R^{d} Rocha L. Computing 59(3): 187207, 1997. Type: Article Rocha presents a strange but intriguing convergence theorem for an iterative process of the form x^{ n + 2} = ( x^{ n + 1} , x^{n} ), for given x^{0} and x^{1<...}

Jun 1 1998 






On a special class of nonlinear Fredholm integral equations of the first kind Schröter T. Computing 58(3): 259279, 1997. Type: Article Urysohn equations of the form _{0}^{1} k ( s, x ( t ) ) dt = y ( s ) , 0 s 1 arise in many areas of application involving the indirect determination of a profile x...

May 1 1998 






Algorithm 768: TENSOLVE: a software package for solving systems of nonlinear equations and nonlinear leastsquares problems using tensor methods Bouaricha A., Schnabel R. ACM Transactions on Mathematical Software 23(2): 174195, 1997. Type: Article For F : &RR;^{n} &RR;^{m}, m n, the problem of minimizing F ( x ) _{ 2} encompasses the nonlinear rootfinding problem (when m = n) and the lea...

Mar 1 1998 






Optimization Polak E., SpringerVerlag New York, Inc., New York, NY, 1997.Type: Book (9780387949710) This monumental treatise is not for the fainthearted or the uninitiated. The prospective reader might well begin by perusing chapter 5, a 97page summary of relevant mathematical background, but should not give up prematurely. The author expounds ...

Nov 1 1997 






Note on the end game in homotopy zero curve tracking Sosonkina M., Watson L., Stewart D. ACM Transactions on Mathematical Software 22(3): 281287, 1996. Type: Article In essence, the homotopy method for solving a system of nonlinear equations f ( x ) = 0 consists of choosing a function h ( x , t ) such that h ( x , 1 ) = f ( x ) and h ( x_{0
} 
Feb 1 1997 






Schwarz iterations for the efficient solution of screen problems with boundary elements Hahne M., Stephan E. Computing 56(1): 6185, 1996. Type: Article The authors draw on material from a variety of sources and their own work to produce preliminary results concerning the convergence of a pair of iterative methods based on domain decomposition (the multiplicative and additive Schwarz methods) for ...

Nov 1 1996 










