Name
Title | ||
|---|---|---|
The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions |
Abstract | ||
|---|---|---|
Numerical techniques based on piecewise polynomial (that is, spline) collation at Gaussian points are exceedingly effective for the approximate solution of boundary value problems, both for ordinary differential equations and for time dependent partial differential equations. There are several widely available computer codes based on this approach, all of which have at their core a particular choice of basis representation for the piecewise polynomials used to approximate the solutions. Until recently, the most popular approach was to use a B-spline representation, but it has been shown that the B-spline basis is inferior, both in operation counts and conditioning, to a certain monomial basis, and the latter has come more into favor. In this paper, we describe a linear algebraic equations which arise in spline collocation at Gaussian points with such a monomial basis. It is shown that the new package, which implements an alternate column and row pivoting algorithm, is a distinct improvement over existing packages from the points of view of speed and storage requirements. In addition, we describe a second package, an important special case of the first, for solving the almost block diagonal systems which arise when condensation is applied to the systems arising in spline collocation at Gaussian points, and also in other methods for solving two-point boundary value problems, such as implicit Runge-Kutta methods and multiple shooting. |
Year | DOI | Venue |
|---|---|---|
1992 | 10.1145/146847.146926 | ACM Trans. Math. Softw. |
Keywords | Field | DocType |
spline collocation,b-spline representation,monomial spline bases,multiple shooting,gaussian point,b-spline basis,basis representation,alternate column and row pivoting,diagonal linear system,approximate solution,certain monomial basis,spline collocation at gaussian points,implicit runge kutta methods,monomial basis function,boundary value problem,almost block diagonal systems,monomial basis,new package,linear algebra,partial differential equation,ordinary differential equation,linear system | Spline (mathematics),Mathematical optimization,Algebra,Polynomial,Orthogonal collocation,Gaussian,Monomial basis,Monomial,Collocation method,Mathematics,Piecewise | Journal |
Volume | Issue | Citations |
18 | 2 | 8 |
PageRank | References | Authors |
1.24 | 6 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gouad Majaess | 1 | 8 | 1.24 |
| Patrick Keast | 2 | 109 | 34.29 |
| Graeme Fairweather | 3 | 165 | 40.42 |
| Karin R. Bennett | 4 | 15 | 1.98 |