Description Usage Arguments Details Value Note References See Also Examples

Estimate the 2-norm of a real (or complex-valued) matrix. 2-norm is also the maximum absolute eigenvalue of M, computed here using the power method.

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`M` |
Numeric matrix; vectors will be considered as column vectors. |

`maxiter` |
Maximum number of iterations allowed; default: 100. |

`tol` |
Tolerance used for stopping the iteration. |

Estimate the 2-norm of the matrix `M`

, typically used for large or
sparse matrices, where the cost of calculating the `norm (A)`

is
prohibitive and an approximation to the 2-norm is acceptable.

Theoretically, the 2-norm of a matrix *M* is defined as

*||M||_2 = max \frac{||M*x||_2}{||x||_2}* for all *x \neq 0*

where *||.||_2* is the Euclidean/Frobenius norm.

2-norm of the matrix as a positive real number.

If feasible, an accurate value of the 2-norm would simply be calculated as the maximum of the singular values (which are all positive):

`max(svd(M)\$d)`

Trefethen, L. N., and D. Bau III. (1997). Numerical Linear Algebra. SIAM, Philadelphia.

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