KpNorm: Difference between revisions
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Created page with "{{Function |name=kpNorm |desc=Computes the (k,p)-norm of an operator |rel=KyFanNorm<br />SchattenNorm<br />TraceNorm |upd=December 1, 2012 |v=1.00}} <tt>'''kpN..." |
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|desc=Computes the [[(k,p)-norm]] of an operator | |desc=Computes the [[(k,p)-norm]] of an operator | ||
|rel=[[KyFanNorm]]<br />[[SchattenNorm]]<br />[[TraceNorm]] | |rel=[[KyFanNorm]]<br />[[SchattenNorm]]<br />[[TraceNorm]] | ||
|upd=December | |upd=December 3, 2012 | ||
|v=1. | |v=1.01}} | ||
<tt>'''kpNorm'''</tt> is a [[List of functions|function]] that computes the [[(k,p)-norm]] of an operator (i.e., the p-norm of the vector of its k largest singular values). It works with both full and sparse matrices. | <tt>'''kpNorm'''</tt> is a [[List of functions|function]] that computes the [[(k,p)-norm]] of an operator (i.e., the p-norm of the vector of its k largest singular values). It works with both full and sparse matrices. | ||
Revision as of 15:12, 3 December 2012
| kpNorm | |
| Computes the (k,p)-norm of an operator | |
| Other toolboxes required | none |
|---|---|
| Related functions | KyFanNorm SchattenNorm TraceNorm |
kpNorm is a function that computes the (k,p)-norm of an operator (i.e., the p-norm of the vector of its k largest singular values). It works with both full and sparse matrices.
Syntax
- NRM = kpNorm(X,K,P)
Argument descriptions
- X: An operator to have its (K,P)-norm computed.
- K: A positive integer.
- P: A real number ≥ 1, or Inf.
Examples
Generalizes the operator, trace, Ky Fan, and Schatten norms
The (K,P)-norm is simply the usual operator norm when K = 1 or P = Inf:
>> X = rand(3);
>> [norm(X), kpNorm(X,1,Inf), kpNorm(X,2,Inf), kpNorm(X,3,Inf), kpNorm(X,1,5)]
ans =
1.0673 1.0673 1.0673 1.0673 1.0673
When P = 1 and K is the size of X, this norm reduces to the trace norm:
>> [kpNorm(X,3,1), TraceNorm(X)] ans = 1.6482 1.6482
More generally, when P = 1 this norm reduces to the Ky Fan K-norm:
>> [kpNorm(X,2,1), KyFanNorm(X,2)] ans = 1.5816 1.5816
Similarly, when K = min(size(X)) this norm reduces to the Schatten P-norm:
>> [kpNorm(X,3,4), SchattenNorm(X,4)] ans = 1.0814 1.0814