Name
Title | ||
|---|---|---|
On polynomial collocation for second kind integral equations with fixed singularities of Mellin type |
Abstract | ||
|---|---|---|
Summary. We consider a polynomial collocation for the numerical solution of a second kind integral equation with an integral kernel
of Mellin convolution type. Using a stability result by Junghanns and one of the authors, we prove that the error of the approximate
solution is less than a logarithmic factor times the best approximation and, using the asymptotics of the solution, we derive
the rates of convergence. Finally, we describe an algorithm to compute the stiffness matrix based on simple Gauß quadratures
and an alternative algorithm based on a recursion in the spirit of Monegato and Palamara Orsi. All together an almost best
approximation to the solution of the integral equation can be computed with 𝒪(n
2[log n]2) resp. 𝒪(n
2) operations, where n is the dimension of the polynomial trial space.
|
Year | DOI | Venue |
|---|---|---|
2003 | 10.1007/s00211-002-0420-2 | Numerische Mathematik |
Keywords | Field | DocType |
integral equation,rate of convergence | Mathematical optimization,Polynomial,Mathematical analysis,Recurrence relation,Convolution,Integral equation,Rate of convergence,Stiffness matrix,Numerical analysis,Mathematics,Collocation | Journal |
Volume | Issue | ISSN |
94 | 2 | 0029-599X |
Citations | PageRank | References |
3 | 0.59 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| G. Mastroianni | 1 | 29 | 7.96 |
| C. Frammartino | 2 | 3 | 0.59 |
| Andreas Rathsfeld | 3 | 8 | 1.96 |