Name
Abstract | ||
|---|---|---|
In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation
rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different
approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the
uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given
which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals.
In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown
coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients,
namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective
function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties.
Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function
may have many local minima, this makes the new approach attractive. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/s11075-007-9077-3 | Numerical Algorithms |
Keywords | Field | DocType |
nonlinear optimization,quadratic program,objective function,local minima,rational function,least squares approximation,satisfiability | Least squares,Mathematical optimization,Polynomial,Mathematical analysis,Interpolation,Maxima and minima,Convex function,Quadratic programming,Rational function,Mathematics,Polynomial and rational function modeling | Journal |
Volume | Issue | ISSN |
45 | 1-4 | 1572-9265 |
Citations | PageRank | References |
11 | 1.15 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Oliver Salazar Celis | 1 | 23 | 3.59 |
| Annie Cuyt | 2 | 161 | 41.48 |
| Brigitte M. Verdonk | 3 | 87 | 27.05 |