Discrete norm approximation of the $L^p$ norm for spline functions
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In Theorem 5.2 in Lynche (1988) "A data reduction strategy for splines with applications to the approximation of functions and data", a bound for the difference between the $(l_2,t)$ and $L^2$ norms is given (Equation 5.8), where $(l_2,t)$ is the discrete weighted norm defined in Equation 5.4.
Could this result be extended to the general $(l_p,t)$ and $L^p$ $(l_2,t)$ norms
for $1leq pleqinfty$? Or at least for $p=1$?
Thanks in advance.
norm approximation spline
asked Nov 16 at 12:14
Fabio.100
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In Theorem 5.2 in Lynche (1988) "A data reduction strategy for splines with applications to the approximation of functions and data", a bound for the difference between the $(l_2,t)$ and $L^2$ norms is given (Equation 5.8), where $(l_2,t)$ is the discrete weighted norm defined in Equation 5.4.
Could this result be extended to the general $(l_p,t)$ and $L^p$ $(l_2,t)$ norms
for $1leq pleqinfty$? Or at least for $p=1$?
Thanks in advance.
norm approximation spline
asked Nov 16 at 12:14
Fabio.100
11
New contributor
Fabio.100 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
In Theorem 5.2 in Lynche (1988) "A data reduction strategy for splines with applications to the approximation of functions and data", a bound for the difference between the $(l_2,t)$ and $L^2$ norms is given (Equation 5.8), where $(l_2,t)$ is the discrete weighted norm defined in Equation 5.4.
Could this result be extended to the general $(l_p,t)$ and $L^p$ $(l_2,t)$ norms
for $1leq pleqinfty$? Or at least for $p=1$?
Thanks in advance.
norm approximation spline
asked Nov 16 at 12:14
Fabio.100
11
New contributor
Fabio.100 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
In Theorem 5.2 in Lynche (1988) "A data reduction strategy for splines with applications to the approximation of functions and data", a bound for the difference between the $(l_2,t)$ and $L^2$ norms is given (Equation 5.8), where $(l_2,t)$ is the discrete weighted norm defined in Equation 5.4.
Could this result be extended to the general $(l_p,t)$ and $L^p$ $(l_2,t)$ norms
for $1leq pleqinfty$? Or at least for $p=1$?
Thanks in advance.
norm approximation spline
norm approximation spline
asked Nov 16 at 12:14
Fabio.100
11
New contributor
Fabio.100 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked Nov 16 at 12:14
Fabio.100
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edited Nov 16 at 14:36
asked Nov 16 at 12:14
Fabio.100
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asked Nov 16 at 12:14
Fabio.100
11
asked Nov 16 at 12:14
Fabio.100
11
11
New contributor
Fabio.100 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Fabio.100 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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