Abstract
An alternative to the matrix inverse procedure is presented. Given a bit register which is arbitrarily large, the matrix inverse to an arbitrarily large matrix can be peformed in
O(
N
2
)
operations, and to matrix multiplication on a vector in
O(N)
. This is in contrast to the usual
O(
N
3
)
and
O(
N
2
)
. A finite size bit register can lead to speeds up of an order of magnitude in large matrices such as
500×500
. The FFT can be improved from
O(NlnN)
to
O(N)
steps, or even fewer steps in a modified butterfly configuration.