Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
On fast multiplication of polynomials over arbitrary algebras
Acta Informatica
On computing determinants of matrices without divisions
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Acceleration of Computation of Determinants and Characteristic Polynomials without Divisions
Cybernetics and Systems Analysis
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Algorithms are proposed for computing the characteristic polynomial, determinant, and adjoint matrix for a n \times n matrix and for solving a system of n-1 linear homogeneous equations in n variables by Cramer's rule using O(n^{4}) ring operations (without the division operation) over an arbitrary commutative ring. The exponent in the estimate of the computation time can be additionally reduced if an algorithm of asymptotically fast matrix multiplication is used.