On matrix inverses modulo a subspace

On the Distribution of Inverses Modulo n

On Newton-Raphson iteration for multiplicative inverses modulo prime powers

We study algorithms for the fast computation of modular inverses. Newton-Raphson iteration over p-adic numbers gives a recurrence relation computing modular inverse modulo p, that is logarithmic in m. We solve the recurrence to obtain an explicit formula for the inverse. Then we study different implementation variants of this iteration and show that our explicit formula is interesting for small...

On generalized inverses of singular matrix pencils

Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate s...

Generalized inverses of a normal matrix

The expressions for generalized inverses of a normal matrix are discussed by its Schur decomposition.

Lookup Structures for Multiplicative Inverses Modulo 2 k

We introduce an inheritance property and related table lookup structures applicable to simplified evaluation of the modular operations “multiplicative inverse”, “discrete log”, and “exponential residue” in the particular modulus 2. Regarding applications, we describe an integer representation system of Benschop for transforming integer multiplications into additions which benefits from our tabl...