Coefficient-free adaptations of polynomial root-finders

Optimal eighth-order simple root-finders free from derivative

The calculation of derivatives of a function mostly takes up a great deal of time and even in some cases, such as the existing problems in engineering and optimization, is impossible to be evaluated directly. Accordingly, an accurate derivative-free class of three-step methods is suggested for solving ( ) = 0. The proposed three-step technique comprises four evaluations of the function per iter...

An Evaluation of Five Polynomial Zero Finders

Coefficient Quantization Error Free Fixed-point Iir Polynomial Predictor Design

In this paper, roundoff noise properties of fixed-point IIR polynomial predictors (FIPPs) and polynomial-predictive differentiators (FIPPDs) are investigated. These filters are designed by augmenting the corresponding FIR basis filters with magnitude response shaping feedbacks. Here we use ideally quantized coefficient (coefficient quantization error free) polynomial FIR predictors (PFPs) or pr...

Polynomial Coefficient Enumeration

Let f(x1, . . . , xk) be a polynomial over a field K. This paper considers such questions as the enumeration of the number of nonzero coefficients of f or of the number of coefficients equal to α ∈ K∗. For instance, if K = Fq then a matrix formula is obtained for the number of coefficients of fn that are equal to α ∈ Fq , as a function of n. Many additional results are obtained related to such ...

A case study for constrained learning neural root finders

This paper makes the detailed analyses of computational complexities and related parameters selection on our proposed constrained learning neural network root-finders including the original feedforward neural network root-finder (FNN-RF) and the recursive partitioning feedforward neural network root-finder (RP-FNN-RF). Specifically, we investigate the case study of the CLA used in neural root-f...