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Anderson, Donald
Harvard University
Cambridge, Massachusetts
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Date Reviewed  
- 10 of 32 reviews

  Uniform pointwise convergence of finite difference schemes using grid equidistribution
Linß T.  Computing 66(1): 27-39, 2001. Type: Article

The issue addressed in this paper is resolving the boundary layer in a model convection-diffusion 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): 373-389, 2000. Type: Article

The basic tool in the verified solution of constrained or unconstrained optimization or root-finding 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): 176-200, 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): 137-144, 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 2-term recursions in Rd
Rocha L.  Computing 59(3): 187-207, 1997. Type: Article

Rocha presents a strange but intriguing convergence theorem for an iterative process of the form x n + 2 = ( x n + 1 , xn ), for given x0 and x1<...

Jun 1 1998  
  On a special class of nonlinear Fredholm integral equations of the first kind
Schröter T.  Computing 58(3): 259-279, 1997. Type: Article

Urysohn equations of the form
01 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 least-squares problems using tensor methods
Bouaricha A., Schnabel R.  ACM Transactions on Mathematical Software 23(2): 174-195, 1997. Type: Article

For F : &RR;n &RR;m, m n, the problem of minimizing F ( x ) 2 encompasses the nonlinear root-finding problem (when m = n) and the lea...

Mar 1 1998  
Polak E.,  Springer-Verlag 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 97-page 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): 281-287, 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 ( x0
Feb 1 1997  
  Schwarz iterations for the efficient solution of screen problems with boundary elements
Hahne M., Stephan E.  Computing 56(1): 61-85, 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  
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