The Exact Condition of the B-Spline Basis May be Hard to Determine
Abstract
The author's conjecture concerning the knot sequence whose associate B-spline sequence has maximum max-norm condition number is disproved. Related condition numbers are explored and the corresponding conjecture concerning the 'worst' knot sequence for them is further supported by numerical results. There is numerical evidence that, in calculations devoted to bounding the p-norm condition number of the (appropriately scaled) B-spline basis, the extreme case occurs for a knot sequence without interior knots, while simple numerical examples show this not to be the case for the max-norm condition number itself. This is disappointing since it is only in the latter case that there seems to be a formula available for the condition number when there are no interior knots. Hence, even if the worst-case conjecture for the bound calculations for the p- norm condition number were proved, it would, offhand, not help in settling the problem of interest.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1988
- Accession Number
- ADA204080
Entities
People
- Carl R. de Boor
Organizations
- University of Wisconsin–Madison