How can I optimize vector normalization in a Molecular Modeling program?

Paul Hughett hughett at
Tue Nov 9 15:17:10 EST 1999

In comp.lang.c Xiaohui Xue <xue at> wrote:
: Instead of l^2 norm, use l^1 norm in your normalization and relevant
: computation.

: For vector {x_n},

: l^2 norm of {x_n} = sqrt( x(1)^2 + x(2)^2 + .... + x(n)^2 ), which
: involves multi and sqrt in the computation.

: l^1 norm of {x_n} = (abs(x(1)) + abs(x(2)) + ... + abs(x(n))), the
: computation of which is simplified.

: In addition, l^1 norm is equivalent to l^2 norm in a strong sense.

The l^1 and l^2 norms are equivalent topologically but not geometrically.
This application is probably geometrical and _requires_ the l^2 norm;
though it's worth looking to see if some approximation to sqrt or the
l^1 norm is good enough.

Paul Hughett

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