Name
Abstract | ||
|---|---|---|
This paper proposes a new preconditioning scheme for a linear system with a saddle-point structure arising from a hybrid approximation scheme on the sphere, an approximation scheme that combines (local) spherical radial basis functions and (global) spherical polynomials. In principle the resulting linear system can be preconditioned by the block-diagonal preconditioner of Murphy, Golub and Wathen. Making use of a recently derived inf–sup condition and the Brezzi stability and convergence theorem for this approximation scheme, we show that in this context the Schur complement in the above preconditioner is spectrally equivalent to a certain non-constant diagonal matrix. Numerical experiments with a non-uniform distribution of data points support the theoretically proved quality of the new preconditioner. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1007/s00211-011-0369-0 | Numerische Mathematik |
Keywords | Field | DocType |
preconditioning. 1,certain non-constant diagonal matrix,approximation scheme,iterative methods,approximation on the sphere,hybrid approximation scheme,linear system,brezzi stability,. radial basis functions,spherical polynomial,new preconditioner,spherical radial basis function,new preconditioning scheme,block-diagonal preconditioner,saddle-point systems,iteration method,radial basis function,schur complement,uniform distribution,numerical analysis,saddle point | Convergence (routing),Saddle,Mathematical optimization,Radial basis function,Polynomial,Preconditioner,Linear system,Mathematical analysis,Diagonal matrix,Schur complement,Mathematics | Journal |
Volume | Issue | ISSN |
118 | 4 | 0945-3245 |
Citations | PageRank | References |
1 | 0.37 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Q. T. Le Gia | 1 | 93 | 12.64 |
| Ian H. Sloan | 2 | 1180 | 183.02 |
| Andrew J. Wathen | 3 | 796 | 65.47 |