The effective condition number applied to error analysis of certain boundary collocation methods. (English) Zbl 0834.65033

This is a detailed study of a certain boundary collocation method for elliptic problems. This method apparently has been in ill repute as being very sensitive to rounding error. The authors demonstrate that even if infinite precision were available, the method is quite ill-posed for quite simple problems arising when attempting to compute an approximation to a harmonic function on quite simple regions. The autoposy of the method is quite thorough.


65F35 Numerical computation of matrix norms, conditioning, scaling
65N38 Boundary element methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65G50 Roundoff error
35J25 Boundary value problems for second-order elliptic equations


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