sva

singular value approximation

Calling Sequence

[U,s,V]=sva(A,k)
[U,s,V]=sva(A,tol)

Arguments

:A real or complex matrix : :k integer : :tol nonnegative real number :

Description

Singular value approximation.

[U,S,V]=sva(A,k) with k an integer >=1, returns U,S and V such that B=U*S*V’ is the best L2 approximation of A with rank( B)= k.

[U,S,V]=sva(A,tol) with tol a real number, returns U,S and V such that B=U*S*V’ such that L2-norm of A-B is at most tol.

Examples

A=`rand`_(5,4)*`rand`_(4,5);
[U,s,V]=sva(A,2);
B=U*s*V';
`svd`_(A)
`svd`_(B)
`clean`_(`svd`_(A-B))

See Also

• svd singular value decomposition