Polynomial Division Template

Chang, Fi‐John

doi:10.9790/3021-021051316

Cited by 3 publications

(1 citation statement)

References 2 publications

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“…A template for polynomial division that returns the quotient and remainder, and is simple and efficient, is described in [6], but it does not consider the effects of errors in the polynomial coefficients. The method for polynomial deconvolution, which is a restricted form of polynomial division when the remainder is identically equal to zero, that is described below enables the effect of perturbations in the polynomial coefficients to be considered.…”

Section: Structured Matrix Methodsmentioning

confidence: 99%

Structured matrix methods for the computation of multiple roots of a polynomial

Winkler

2014

Journal of Computational and Applied Mathematics

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This paper considers the application of structured matrix methods for the computation of multiple roots of a polynomial. In particular, the given polynomial f (y) is formed by the addition of noise to the coefficients of its exact formf (y), and the noise causes multiple roots off (y) to break up into simple roots. It is shown that structured matrix methods enable the simple roots of f (y) that originate from the same multiple root off (y) to be 'sewn' together, which therefore allows the multiple roots off (y) to be computed. The algorithm that achieves these results involves several greatest common divisor computations and polynomial deconvolutions, and special care is required for the implementation of these operations because they are ill-posed. Computational examples that demonstrate the theory are included, and the results are compared with the results from MultRoot, which is a suite of Matlab programs for the computation of multiple roots of a polynomial.

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Section: Structured Matrix Methodsmentioning

confidence: 99%

Structured matrix methods for the computation of multiple roots of a polynomial

Winkler

2014

Journal of Computational and Applied Mathematics

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On partial fraction decompositions by repeated polynomial divisions

Man

2017

International Journal of Mathematical Education in Science and

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Characteristics of the Protoporphyrin IX Binding Sites on Human Serum Albumin Using Molecular Docking

Sułkowski¹,

Pawełczak

Chudzik

et al. 2016

Molecules

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Human serum albumin (HSA) is the main plasma protein responsible for a distribution of drugs in the human circulatory system. The binding to HSA is one of the factors that determines both the pharmacological actions and the side effects of drugs. The derivative of heme, protoporphyrin IX (PpIX), is a hydrophobic photosensitizer widely used in photodynamic diagnosis and therapy of various malignant disorders. Using absorption and fluorescence spectroscopy, it has been demonstrated that PpIX forms complexes with HSA. Its binding sites in the tertiary structure of HSA were found in the subdomains IB and IIA. PpIX binds to HSA in one class of binding sites with the association constant of 1.68 × 10 5 M −1 and 2.30 × 10 5 M −1 for an excitation at wavelength λ ex = 280 nm and 295 nm, respectively. The binding interactions between HSA and PpIX have been studied by means of molecular docking simulation using the CLC Drug Discovery Workbench (CLC DDWB) computer program. PpIX creates a strong 'sandwich-type' complex between its highly conjugated porphine system and aromatic side chains of tryptophan and tyrosine. In summary, fluorescent studies on binding interactions between HSA and PpIX have been confirmed by the results of computer simulation.

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Polynomial Division Template

Abstract: Abstract--The compact template for the division of two univariate polynomials to find the quotient and reminder is derived. The process is very simple, efficient and direct, comparing to the familiar classical long polynomial division and synthetic polynomial division.

Cited by 3 publications

References 2 publications

Structured matrix methods for the computation of multiple roots of a polynomial

Structured matrix methods for the computation of multiple roots of a polynomial

On partial fraction decompositions by repeated polynomial divisions

Characteristics of the Protoporphyrin IX Binding Sites on Human Serum Albumin Using Molecular Docking

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