David K. Probst

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This paper presents an improved adaptive hybrid algorithm for multiplying dense multivariate polynomials that is both time and space efficient. The hybrid algorithm makes use of two families of univariate algorithms, one Karatsuba based and the other DFT based, which are applied recursively to solve the multivariate problem. The hybrid algorithm is adaptive(More)
We discuss four new algorithms from a family of algorithms for computing integer powers of sparse polynomials. The four algorithms form a sequence of successively better algorithms; even the first member of the sequence shows an improvement in the leading term of the cost function in comparison with the best previously known binomial-expansion algorithm. To(More)
BACKGROUND Currently, glycemic management for individuals with diabetes mellitus involves monitoring glucose only, which is insufficient as glucose metabolism involves other biomarkers such as insulin. Monitoring additional biomarkers alongside glucose has been proposed to improve glycemic control. In this work, the development of a rapid and label-free(More)