| BCH decoding usually involves the evaluation of the error-locator polynomial. This is often achieved with the Berlekamp-Massey algorithm. The evaluation of the error-locator polynomial may also be computed using fast inversion techniques for Hankel matrices. It can be shown that O(lt) steps are necessary, with l being the number of errors which occurred and t being the error-correction capabi...

In this paper we review some applications of generalized polynomial chaos expansion for uncertainty quantification. The mathematical framework is presented and the convergence of the method is demonstrated for model problems. In particular, we solve the first-order and second-order ordinary differential equations with random parameters, and examine the efficiency of generalized polynomial chaos...

An efficient algorithm for evaluating the matrix polynomial I + A + A + ••• +A~ is developed. The proposed scheme is simple and eliminates the difficulties encountered in applying a recently reported procedure [11.

A n-dimensional Lie group G equipped with a left invariant symplectic form ω+ is called a symplectic Lie group. It is well-known that ω+ induces a left invariant affine structure on G. Relatively to this affine structure we show that the left invariant Poisson tensor π+ corresponding to ω+ is polynomial of degree 1 and any right invariant k-multivector field on G is polynomial of degree at most...

BCH decoding usually involves the evaluation of the error-locator polynomial. This is often achieved with the Berlekamp-Massey algorithm, which requires about O(t) computational steps, where t is the error-correction capability of the BCH code. The evaluation of the errorlocator polynomial may also be computed using fast inversion techniques for Hankel matrices. It will be shown that only O(lt)...

This paper extends the modified affine arithmetic in matrix form method for bivariate polynomial evaluation and algebraic curve plotting in 2D to modified affine arithmetic in tensor form for trivariate polynomial evaluation and algebraic surface plotting in 3D. Experimental comparison shows that modified affine arithmetic in tensor form is not only more accurate but also much faster than stand...