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
|req=[[kpNorm]]
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|rel=[[kpNorm]]<br />[[SchattenNorm]]<br />[[TraceNorm]]
|rel=[[SchattenNorm]]<br />[[TraceNorm]]
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|cat=[[List of functions#Norms|Norms]]
 
|upd=December 1, 2012
 
|upd=December 1, 2012
|v=1.00}}
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|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:
<pre>
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<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.
</pre>
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</syntaxhighlight>
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{{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.