Method on @infsup: norm (A, P)

Method on @infsup: norm (A, P, Q)

Method on @infsup: norm (A, P, OPT)

Compute the p-norm (or p,q-norm) of the matrix A.

If A is a matrix:

P = 1

1-norm, the largest column sum of the absolute values of A.

P = inf

Infinity norm, the largest row sum of the absolute values of A.

P = "fro"

Frobenius norm of A, sqrt (sum (diag (A' * A))).

If A is a vector or a scalar:

P = inf

max (abs (A)).

P = -inf

min (abs (A)).

P = "fro"

Frobenius norm of A, sqrt (sumsq (abs (A))).

P = 0

Hamming norm - the number of nonzero elements.

other P, P > 1

p-norm of A, (sum (abs (A) .^ P)) ^ (1/P).

other P, P < 1

p-pseudonorm defined as above.

It Q is used, compute the subordinate matrix norm induced by the vector p-norm and vector q-norm. The subordinate p,q-norm is defined as the maximum of norm (A * x, Q), where x can be chosen such that norm (x, P) = 1. For P = 1 and Q = inf this is the max norm, max (max (abs (A))).

If OPT is the value "rows", treat each row as a vector and compute its norm. The result returned as a column vector. Similarly, if OPT is "columns" or "cols" then compute the norms of each column and return a row vector.

Accuracy: The result is a valid enclosure.

norm (infsup (magic (3)), "fro")
  ⇒ ans ⊂ [16.881, 16.882]

norm (infsup (magic (3)), 1, "cols")
  ⇒ ans = 1×3 interval vector

       [15]   [15]   [15]

See also: @infsup/abs, @infsup/max.

Package: interval