`normest1`

Estimate of the 1-norm of a matrix.

Category: Other public functions: matfun

Syntax

est = normest1(A)

Estimates norm(A, 1), the largest absolute column sum.

[est, v] = normest1(A)

Also returns a vector v for which the estimate is attained.

Description

The 1-norm of a large matrix costs time proportional to the number of entries. normest1 uses a few matrix-vector products instead, which is cheaper for large or sparse matrices, and is the building block of condest. For small matrices the answer is usually the exact value.

Input arguments

A: Square matrix, which may be sparse.

Output arguments

est: Estimated 1-norm.
v: Vector related to the estimate.

Example

Compare with norm

A = magic(4);
normest1(A)
norm(A, 1)

Output

ans = 34
ans = 34

normest1