Finite difference preconditioning cubic spline collocation method of elliptic equations

We discuss a finite difference preconditioner for the C-1 interpolatory cubic spline collocation method for a uniformly elliptic operator A defined by Au := -Delta u + a(0)u in Omega (the unit square) with homogeneous Dirichlet boundary conditions. Using the generalized field of values arguments, we discuss the eigenvalues of the preconditioned matrix (L) over cap(N2)(-1)(A) over cap(N2) where (A) over cap(N2) is the matrix of the collocation discretization operator A(N2) corresponding to A, and (L) over cap(N2) is the matrix of the finite difference operator L-N2 corresponding to the uniformly elliptic operator L given by Lv := -Delta v + v in Omega with homogeneous Dirichlet boundary conditions. Finally we mention a bound of H-1-singular values of (L) over cap(N2)(-1)(A) over cap(N2) for a general elliptic operator Au := -Delta u + a(1)u(x) + a(2)u(y) + a(0)u in Omega.
Publisher
SPRINGER VERLAG
Issue Date
1997-07
Language
ENG
Citation

NUMERISCHE MATHEMATIK, v.77, no.1, pp.83 - 103

ISSN
0029-599X
URI
http://hdl.handle.net/10203/73615
Appears in Collection
MA-Journal Papers(저널논문)
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