What is the support of a basis function?
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I'm a reading a paper on surface interpolation [1].
However, there is a term that I cannot make sense of and I cannot find it via Google either. The text reads as follows:
The discrete equations we developed in the section were obtained using nodal basis functions, which have local support. This makes the computation of the discrete equations easier (more uniform), and results in a set of sparse equations, which are essential for a massively parallel implementation. An alternative to these nodal basis functions are the hierarchical basis functions developed by Yserentant. In this approach, the usual nodal basis set x is replaced by a hierarchical basis set y. Certain elements of the hierarchical basis set have larger support than the nodal basis elements, which allows the relaxation algorithm to converge more quickly when using the hierarchical set.
What does support mean when it comes to basis functions?
terminology
asked Dec 10 '18 at 21:35
Saad AbbasiSaad Abbasi
1215
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add a comment |
$begingroup$
I'm a reading a paper on surface interpolation [1].
However, there is a term that I cannot make sense of and I cannot find it via Google either. The text reads as follows:
The discrete equations we developed in the section were obtained using nodal basis functions, which have local support. This makes the computation of the discrete equations easier (more uniform), and results in a set of sparse equations, which are essential for a massively parallel implementation. An alternative to these nodal basis functions are the hierarchical basis functions developed by Yserentant. In this approach, the usual nodal basis set x is replaced by a hierarchical basis set y. Certain elements of the hierarchical basis set have larger support than the nodal basis elements, which allows the relaxation algorithm to converge more quickly when using the hierarchical set.
What does support mean when it comes to basis functions?
terminology
asked Dec 10 '18 at 21:35
Saad AbbasiSaad Abbasi
1215
$endgroup$
$begingroup$
Support of a function generally means the subset of the domain where the function is not zero. IDK what local support means but I think it means the support is a bounded set.. does that help?
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– mm-crj
Dec 10 '18 at 21:41
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Yes it exactly means that. en.wikipedia.org/wiki/B-spline#Properties
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– mm-crj
Dec 10 '18 at 21:44
$begingroup$
A response would do no harm you know?
$endgroup$
– mm-crj
Dec 10 '18 at 22:23
add a comment |
$begingroup$
I'm a reading a paper on surface interpolation [1].
However, there is a term that I cannot make sense of and I cannot find it via Google either. The text reads as follows:
The discrete equations we developed in the section were obtained using nodal basis functions, which have local support. This makes the computation of the discrete equations easier (more uniform), and results in a set of sparse equations, which are essential for a massively parallel implementation. An alternative to these nodal basis functions are the hierarchical basis functions developed by Yserentant. In this approach, the usual nodal basis set x is replaced by a hierarchical basis set y. Certain elements of the hierarchical basis set have larger support than the nodal basis elements, which allows the relaxation algorithm to converge more quickly when using the hierarchical set.
What does support mean when it comes to basis functions?
terminology
asked Dec 10 '18 at 21:35
Saad AbbasiSaad Abbasi
1215
$endgroup$
I'm a reading a paper on surface interpolation [1].
However, there is a term that I cannot make sense of and I cannot find it via Google either. The text reads as follows:
The discrete equations we developed in the section were obtained using nodal basis functions, which have local support. This makes the computation of the discrete equations easier (more uniform), and results in a set of sparse equations, which are essential for a massively parallel implementation. An alternative to these nodal basis functions are the hierarchical basis functions developed by Yserentant. In this approach, the usual nodal basis set x is replaced by a hierarchical basis set y. Certain elements of the hierarchical basis set have larger support than the nodal basis elements, which allows the relaxation algorithm to converge more quickly when using the hierarchical set.
What does support mean when it comes to basis functions?
terminology
terminology
asked Dec 10 '18 at 21:35
Saad AbbasiSaad Abbasi
1215
asked Dec 10 '18 at 21:35
Saad AbbasiSaad Abbasi
1215
asked Dec 10 '18 at 21:35
Saad AbbasiSaad Abbasi
1215
asked Dec 10 '18 at 21:35
Saad AbbasiSaad Abbasi
1215
asked Dec 10 '18 at 21:35
Saad AbbasiSaad Abbasi
1215
1215
$begingroup$
Support of a function generally means the subset of the domain where the function is not zero. IDK what local support means but I think it means the support is a bounded set.. does that help?
$endgroup$
– mm-crj
Dec 10 '18 at 21:41
$begingroup$
Yes it exactly means that. en.wikipedia.org/wiki/B-spline#Properties
$endgroup$
– mm-crj
Dec 10 '18 at 21:44
$begingroup$
A response would do no harm you know?
$endgroup$
– mm-crj
Dec 10 '18 at 22:23
add a comment |
$begingroup$
Support of a function generally means the subset of the domain where the function is not zero. IDK what local support means but I think it means the support is a bounded set.. does that help?
$endgroup$
– mm-crj
Dec 10 '18 at 21:41
$begingroup$
Yes it exactly means that. en.wikipedia.org/wiki/B-spline#Properties
$endgroup$
– mm-crj
Dec 10 '18 at 21:44
$begingroup$
A response would do no harm you know?
$endgroup$
– mm-crj
Dec 10 '18 at 22:23
$begingroup$
Support of a function generally means the subset of the domain where the function is not zero. IDK what local support means but I think it means the support is a bounded set.. does that help?
$endgroup$
– mm-crj
Dec 10 '18 at 21:41
$begingroup$
Support of a function generally means the subset of the domain where the function is not zero. IDK what local support means but I think it means the support is a bounded set.. does that help?
$endgroup$
– mm-crj
Dec 10 '18 at 21:41
$begingroup$
Yes it exactly means that. en.wikipedia.org/wiki/B-spline#Properties
$endgroup$
– mm-crj
Dec 10 '18 at 21:44
$begingroup$
Yes it exactly means that. en.wikipedia.org/wiki/B-spline#Properties
$endgroup$
– mm-crj
Dec 10 '18 at 21:44
$begingroup$
A response would do no harm you know?
$endgroup$
– mm-crj
Dec 10 '18 at 22:23
$begingroup$
A response would do no harm you know?
$endgroup$
– mm-crj
Dec 10 '18 at 22:23
add a comment |
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$begingroup$
Support of a function generally means the subset of the domain where the function is not zero. IDK what local support means but I think it means the support is a bounded set.. does that help?
$endgroup$
– mm-crj
Dec 10 '18 at 21:41
$begingroup$
Yes it exactly means that. en.wikipedia.org/wiki/B-spline#Properties
$endgroup$
– mm-crj
Dec 10 '18 at 21:44
$begingroup$
A response would do no harm you know?
$endgroup$
– mm-crj
Dec 10 '18 at 22:23