We show that any regular quadratic matrix polynomial can be reduced to an upper triangular quadratic matrix polynomial over the complex numbers preserving the finite and infinite elementary divisors. We characterize the real quadratic matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal bloc...

Coded computing is an effective technique to mitigate “stragglers” in large-scale and distributed matrix multiplication. In particular, univariate polynomial codes have been shown be straggler mitigation by making the computation time depend only on fastest workers. However, these schemes completely ignore work done straggling workers resulting a waste of computational resources. To reduce amou...

We consider the problem of secure distributed matrix multiplication (SDMM). Coded computation has been shown to be an effective solution in multiplication, both providing privacy against workers and boosting speed by efficiently mitigating stragglers. In this work, we present a non-direct extension recently introduced bivariate polynomial codes. Bivariate codes have able further up exploiting p...

A method is developed to compute the zeros of a quaternion polynomial with all terms of the form ok Xk. This method is based essentially in Niven’s algorithm (11, which consists of dividing the polynomial by a characteristic polynomial associated to a zero. The information about the trace and the norm of the zero is obtained by an original idea which requires the companion matrix associated to ...