Compute the infinitity norm of a matrix
This function returns the ≤ft\| {\mathbf{x}} \right\|_∞ norm of the matrix {\mathbf{x}}.
inf.norm(x)
x |
a numeric vector or matrix |
Let {\bf{x}} be an m \times n numeric matrix. The formula used to compute the norm is ≤ft\| {\bf{x}} \right\|_∞ = \mathop {\max }\limits_{1 ≤ i ≤ m} ∑\limits_{j = 1}^n {≤ft| {x_{i,j} } \right|} . This is merely the maximum absolute row sum of the m \times n maxtris.
A numeric value.
Frederick Novomestky fnovomes@poly.edu
Bellman, R. (1987). Matrix Analysis, Second edition, Classics in Applied Mathematics, Society for Industrial and Applied Mathematics.
Golub, G. H. and C. F. Van Loan (1996). Matrix Computations, Third Edition, The John Hopkins University Press.
Horn, R. A. and C. R. Johnson (1985). Matrix Analysis, Cambridge University Press.
A <- matrix( c( 3, 5, 7, 2, 6, 4, 0, 2, 8 ), nrow=3, ncol=3, byrow=TRUE ) print( inf.norm( A ) )
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