Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

A Mesh-Independence Principle for Operator Equations and Their Discretizations

E. L. Allgower, K. Bohmer, F. A. Potra and W. C. Rheinboldt
SIAM Journal on Numerical Analysis
Vol. 23, No. 1 (Feb., 1986), pp. 160-169
Stable URL: http://www.jstor.org/stable/2157457
Page Count: 10
  • Subscribe ($19.50)
  • Cite this Item
A Mesh-Independence Principle for Operator Equations and Their Discretizations
Preview not available

Abstract

The mesh-independence principle asserts that, when Newton's method is applied to a nonlinear equation between some Banach spaces as well as to some finite-dimensional discretization of that equation, then the behavior of the discretized process is asymptotically the same as that for the original iteration and, as a consequence, the number of steps required by the two processes to converge to within a given tolerance is essentially the same. So far this result has been proved only for certain classes of boundary value problems. In this paper a proof is presented for a general class of operator equations and discretizations. It covers the earlier results and extends them well beyond the cases that have been considered before.

Page Thumbnails

  • Thumbnail: Page 
160
    160
  • Thumbnail: Page 
161
    161
  • Thumbnail: Page 
162
    162
  • Thumbnail: Page 
163
    163
  • Thumbnail: Page 
164
    164
  • Thumbnail: Page 
165
    165
  • Thumbnail: Page 
166
    166
  • Thumbnail: Page 
167
    167
  • Thumbnail: Page 
168
    168
  • Thumbnail: Page 
169
    169