Difference between revisions of "KyFanNorm"
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|name=KyFanNorm | |name=KyFanNorm | ||
|desc=Computes the [[Ky Fan norm|Ky Fan k-norm]] of an operator | |desc=Computes the [[Ky Fan norm|Ky Fan k-norm]] of an operator | ||
| − | | | + | |rel=[[kpNorm]]<br />[[SchattenNorm]]<br />[[TraceNorm]] |
| − | + | |cat=[[List of functions#Norms|Norms]] | |
|upd=December 1, 2012 | |upd=December 1, 2012 | ||
| − | |v= | + | |v=0.50}} |
<tt>'''KyFanNorm'''</tt> is a [[List of functions|function]] that computes the [[Ky Fan norm|Ky Fan k-norm]] of an operator (i.e., the sum of its k largest singular values). It works with both full and sparse matrices. | <tt>'''KyFanNorm'''</tt> is a [[List of functions|function]] that computes the [[Ky Fan norm|Ky Fan k-norm]] of an operator (i.e., the sum of its k largest singular values). It works with both full and sparse matrices. | ||
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===Equals the operator norm when <tt>K = 1</tt> (but faster!)=== | ===Equals the operator norm when <tt>K = 1</tt> (but faster!)=== | ||
The Ky Fan 1-norm is just the operator norm, which is implemented in MATLAB by the <tt>[http://www.mathworks.com/help/symbolic/norm.html norm]</tt> function. However, the <tt>KyFanNorm</tt> function is typically faster than the <tt>norm</tt> function: | The Ky Fan 1-norm is just the operator norm, which is implemented in MATLAB by the <tt>[http://www.mathworks.com/help/symbolic/norm.html norm]</tt> function. However, the <tt>KyFanNorm</tt> function is typically faster than the <tt>norm</tt> function: | ||
| − | < | + | <syntaxhighlight> |
>> X = rand(2500); | >> X = rand(2500); | ||
>> tic; KyFanNorm(X,1) | >> tic; KyFanNorm(X,1) | ||
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Elapsed time is 4.288788 seconds. | Elapsed time is 4.288788 seconds. | ||
| − | </ | + | </syntaxhighlight> |
| + | |||
| + | {{SourceCode|name=KyFanNorm}} | ||
Revision as of 16:37, 22 September 2014
| KyFanNorm | |
| Computes the Ky Fan k-norm of an operator | |
| Other toolboxes required | none |
|---|---|
| Related functions | kpNorm SchattenNorm TraceNorm |
| Function category | Norms |
KyFanNorm is a function that computes the Ky Fan k-norm of an operator (i.e., the sum of its k largest singular values). It works with both full and sparse matrices.
Syntax
- NRM = KyFanNorm(X,K)
Argument descriptions
- X: An operator to have its Ky Fan K-norm computed.
- K: A positive integer.
Examples
Equals the operator norm when K = 1 (but faster!)
The Ky Fan 1-norm is just the operator norm, which is implemented in MATLAB by the norm function. However, the KyFanNorm function is typically faster than the norm function:
>> X = rand(2500);
>> tic; KyFanNorm(X,1)
toc
ans =
1250.2
Elapsed time is 0.861377 seconds.
>> tic; norm(X)
toc
ans =
1250.2
Elapsed time is 4.288788 seconds.Source code
Click here to view this function's source code on github.