$[t_j,t_{j+1},…,t_{j+k}]f$ Divided Difference on B-splines.
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While reading Moments and Fourier Transform of B-splines (Neuman,E.) I found a different notation for the B-splines.
The author define $M_{j,k}(x)$ with knots $t_j<t_{j+1}<...<t_{j+k}$ as:
$$M_{j,k}(x)=k[t_j,t_{j+1},...,t_{j+k}](.-x)_+^{k-1}$$
where $[t_j,t_{j+1},...,t_{j+k}]f$ is said to be the k-th divided difference for f.
Is this notation equivalent to the traditional way to express B-splines? I honestly cannot see the common points. Any hint or suggestion will be greatly appreciated.
functional-analysis interpolation spline
asked Nov 21 at 18:26
Ramiro Scorolli
64513
add a comment |
up vote
0
down vote
favorite
While reading Moments and Fourier Transform of B-splines (Neuman,E.) I found a different notation for the B-splines.
The author define $M_{j,k}(x)$ with knots $t_j<t_{j+1}<...<t_{j+k}$ as:
$$M_{j,k}(x)=k[t_j,t_{j+1},...,t_{j+k}](.-x)_+^{k-1}$$
where $[t_j,t_{j+1},...,t_{j+k}]f$ is said to be the k-th divided difference for f.
Is this notation equivalent to the traditional way to express B-splines? I honestly cannot see the common points. Any hint or suggestion will be greatly appreciated.
functional-analysis interpolation spline
asked Nov 21 at 18:26
Ramiro Scorolli
64513
There is this paper available web.stanford.edu/class/cme324/classics/deboor.pdf, which proves the recurrence relation from what you wrote.
– Oppenede
Nov 22 at 12:48
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
While reading Moments and Fourier Transform of B-splines (Neuman,E.) I found a different notation for the B-splines.
The author define $M_{j,k}(x)$ with knots $t_j<t_{j+1}<...<t_{j+k}$ as:
$$M_{j,k}(x)=k[t_j,t_{j+1},...,t_{j+k}](.-x)_+^{k-1}$$
where $[t_j,t_{j+1},...,t_{j+k}]f$ is said to be the k-th divided difference for f.
Is this notation equivalent to the traditional way to express B-splines? I honestly cannot see the common points. Any hint or suggestion will be greatly appreciated.
functional-analysis interpolation spline
asked Nov 21 at 18:26
Ramiro Scorolli
64513
While reading Moments and Fourier Transform of B-splines (Neuman,E.) I found a different notation for the B-splines.
The author define $M_{j,k}(x)$ with knots $t_j<t_{j+1}<...<t_{j+k}$ as:
$$M_{j,k}(x)=k[t_j,t_{j+1},...,t_{j+k}](.-x)_+^{k-1}$$
where $[t_j,t_{j+1},...,t_{j+k}]f$ is said to be the k-th divided difference for f.
Is this notation equivalent to the traditional way to express B-splines? I honestly cannot see the common points. Any hint or suggestion will be greatly appreciated.
functional-analysis interpolation spline
functional-analysis interpolation spline
asked Nov 21 at 18:26
Ramiro Scorolli
64513
asked Nov 21 at 18:26
Ramiro Scorolli
64513
asked Nov 21 at 18:26
Ramiro Scorolli
64513
asked Nov 21 at 18:26
Ramiro Scorolli
64513
asked Nov 21 at 18:26
Ramiro Scorolli
64513
64513
There is this paper available web.stanford.edu/class/cme324/classics/deboor.pdf, which proves the recurrence relation from what you wrote.
– Oppenede
Nov 22 at 12:48
add a comment |
There is this paper available web.stanford.edu/class/cme324/classics/deboor.pdf, which proves the recurrence relation from what you wrote.
– Oppenede
Nov 22 at 12:48
There is this paper available web.stanford.edu/class/cme324/classics/deboor.pdf, which proves the recurrence relation from what you wrote.
– Oppenede
Nov 22 at 12:48
There is this paper available web.stanford.edu/class/cme324/classics/deboor.pdf, which proves the recurrence relation from what you wrote.
– Oppenede
Nov 22 at 12:48
add a comment |
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There is this paper available web.stanford.edu/class/cme324/classics/deboor.pdf, which proves the recurrence relation from what you wrote.
– Oppenede
Nov 22 at 12:48