Spline Toolbox

Index

Numerics

1-column matrix

A

almost block-diagonal

collocation matrix

appropriate knot sequence

use <1> <2> <3> <4> <5> <6> <7>

augmented knot sequence

B

banded linear system

as set in ppmak

cautionary note <1> <2>

extension outside

for the pp-form

use in

basis function

of thin-plate spline

best interpolant

conversion to ppform

introduction to

smoothness conditions

bicubic spline example <1> <2>

break

break sequence

example <1> <2>

breaks (Glossary)

breaks vs knots

B-representation

B-spline

example <1> <2>

some sample figures

C

center

of a shifted power form

Chebyshev polynomial

Chebyshev spline

circle, spline approximation to

clamped end condition

constructed in spcol

collocation matrix

composing function with a matrix

constructive approach to splines

control point

of a spline curve

control polygon

conversion

B-form to ppform

via splpp,sprpp

coordinates with respect to a basis

B-spline

smoothing spline

spline

cubic means order 4

cubic smoothing spline

cubic spline

cubic spline curve

cubic spline interpolation

Curry-Schoenberg Theorem

plotted via fnplt

D

multiplicity

degrees of freedom

derivative

of a rational spline

differential equation

solved with splines

differentiation

in the pp sense

discrete

differentiation

least-squares approximation

domain of a function

draftsman's spline

dual functional

E

end

variational <1> <2>

error measure

in splinetool

evaluation

of tensor product spline

extension beyond basic interval

cautionary note

F

use <1> <2> <3>

use <1> <2> <3>

use <1> <2> <3> <4>

use <1> <2> <3> <4>

Franke function

functional

G

good interpolation sites

from Chebyshev spline

graphic accuracy

gridded data

example <1> <2>

H

Hermite

Hermite interpolation

I

integral

integral equation

interior

interpolant

variational

by thin-plate spline

Hermite <1> <2>

interpolation points, good

interval notation (glossary)

J

jump

ignored in fnder

K

average

insertion

used in fn2fm

used in spcrv

used in splpp

cautionary note 3-47

multiplicity vs smoothness

sequence

of a spline (glossary)

simple (glossary)

knots vs breaks

L

Lagrange end condition

least-squares

approximation

discrete

via slvblk 3-71

limit from the left

limit from the right

linear

combination of functions

local

polynomial coefficients

power form

M

matrix

maximum

minimum

multiplicity

of a data point

of a knot <1> <2>

of smoothness conditions

vs smoothness

N

naming conventions

natural

nested multiplication

Newton's method

nonlinear system

normalized B-spline

not-a-knot end condition

O

optimal

of a polynomial

P

curve

parametric

cubic spline curve

parametrization

piecewise cubic

piecewise-polynomial

placeholder notation

polynomial part of stform

ppform

conversion from B-form

introduction to

pp-representation

Q

QR factorization

use in slvblk

quadratic convergence

R

radial basis function <1> <2>

range of a function

rational spline

from rpmak,rspmak

recovery scheme

recurrence relation

Remez algorithm

restriction to an interval

roughness measure

in splinetool

roughness weight

S

scalar-valued vs vector-valued

scaling of a function

scattered

data

Schoenberg <1> <2>

Schoenberg-Whitney

conditions

theorem

shifted power form

side conditions

parameter

multiplicity of

use <1> <2> <3> <4> <5>

use <1> <2> <3>

sparse

use <1> <2> <3> <4> <5> <6>

sphere

spline

approximation to a circle

curve

use <1> <2> <3> <4> <5> <6> <7>

staircase shape

stform

support of a B-spline

T

target of a function

Taylor

polynomial

tensor product <1> <2>

thin-plate spline

typographical conventions (table)

U

uniform

uniqueness of B-form

univariate vs multivariate

V

value outside basic interval

approach to splines

interpolant

vector

in this toolbox

is always a column matrix

-valued

vs scalar-valued

W

Glossary