Abstract
We prove that some central problems in computational linear algebra are in the complexity class RNC 1 that is solvable by uniform families of probabilistic boolean circuits of logarithmic depth and polynomial size. In particular, we first show that computing the solution of n × n linear systems in the form x = B x + c, with | B| ∞ ≤ 1 − n − k , k = O(1), in the fixed precision model (i.e., computing d = O(1) digits of the result) is in RNC 1 ; then we prove that the case of general n × n linear systems A x = b, with both | A| ∞ and | b| ∞ bounded by polynomials in n, can be reduced to the special case mentioned before.
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