Francesco Aldo Costabile's Books

Polynomial Sequences

Basic Methods, Special Classes, and Computational Applications

By: Francesco Aldo Costabile,Maria Italia Gualtieri,Anna Napoli

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Polynomial Sequences

Basic Methods, Special Classes, and Computational Applications

By: Francesco Aldo Costabile,Maria Italia Gualtieri,Anna Napoli

Polynomials are useful mathematical tools. They are simply defined and can be calculated quickly on computer systems. They can be differentiated and integrated easily and can be pieced together to form spline curves. After Weierstrass approximation Theorem, polynomial sequences have acquired considerable importance not only in the various branches of Mathematics, but also in Physics, Chemistry and Engineering disciplines. There is a wide literature on specific polynomial sequences. But there is no literature that attempts a systematic exposition of the main basic methods for the study of a generic polynomial sequence and, at the same time, gives an overview of the main polynomial classes and related applications, at least in numerical analysis. In this book, through an elementary matrix calculus-based approach, an attempt is made to fill this gap by exposing dated and very recent results, both theoretical and applied.

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Page Count

526

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110757249

ISBN 13

9783110757248

Modern Umbral Calculus

An Elementary Introduction with Applications to Linear Interpolation and Operator Approximation Theory

By: Francesco Aldo Costabile

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Modern Umbral Calculus

An Elementary Introduction with Applications to Linear Interpolation and Operator Approximation Theory

By: Francesco Aldo Costabile

This book presents a novel approach to umbral calculus, which uses only elementary linear algebra (matrix calculus) based on the observation that there is an isomorphism between Sheffer polynomials and Riordan matrices, and that Sheffer polynomials can be expressed in terms of determinants. Additionally, applications to linear interpolation and operator approximation theory are presented in many settings related to various families of polynomials.

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