MATINF 4170/9170 - Lecture 9 - 15/3-2017Last time: Chapter 4• Weekly problem 3.2• Knot insertion• Blossoms
Today: Chapter 4 • Recap: Blossoms• Knot insertion• Sign changes
Previously, for
In particular
The B-spline coefficients are functions of the knots
by the blossom
Spline coefficients for polynomials
Inserting one knot
Inserting several knots
Simple knot insertion matrices
• two-banded (n+1)xn matrix• nonzero elements• rows sum to one (row stochastic)
General knot insertion matrices
Descartes rule of signsRecall: z is a zero of f with multiplicity r>0 if
Spline sign changes
Spline sign changes
Spline sign changes