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A standard way of implementing Huffman’s optimal code construction algorithm is by using a sorted sequence of frequencies. Several aspects of the algorithm are investigated as to the consequences of relaxing the requirement of keeping the frequencies in order. Using only partial order may speed...
It is well known that in the computation of Gröbner bases arbitrarily small perturbations in the coefficients of polynomials may lead to a completely different staircase, even if the solutions of the polynomial system change continuously. This phenomenon is called artificial discontinuity in...
Sturmfels offered 100 Swiss Francs in 2005 to a conjecture, which deals with a special case of the maximum likelihood estimation for a latent class model. This paper confirms the conjecture positively.
We study the problem of optimizing over parameters a particular real root of a polynomial with parametric coefficients. We propose an efficient symbolic method for solving the optimization problem based on a special cylindrical algebraic decomposition algorithm, which asks for a semi-algebraic...
A new numerical approach to compute all real roots of a system of two bivariate polynomial equations over a given box is described. Using the Bernstein–Bézier representation, we compute the best linear approximant and the best quadratic approximant of the two polynomials with respect to the L
We develop an eighth order family of methods, consisting of three steps and three parameters, for solving nonlinear equations. Per iteration the methods require four evaluations (three function evaluations and one evaluation of the first derivative). Convergence analysis shows that the family is...
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