Weighted Polynomial Approximation and Numerical Methods for Integral Equations

Peter Junghanns, Giuseppe Mastroianni, Incoronata Notarangelo

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English

Springer Nature Switzerland AG
13 August 2022

Integral calculus & equations

Series: Pathways in Mathematics

The book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.

By: Peter Junghanns, Giuseppe Mastroianni, Incoronata Notarangelo
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 2021 ed.
Dimensions: Height: 235mm, Width: 155mm,
Weight: 1.009kg
ISBN: 9783030774998
ISBN 10: 3030774996
Series: Pathways in Mathematics
Pages: 658
Publication Date: 13 August 2022
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Peter Junghanns is Professor Emeritus at the Mathematics Department of the Technical University of Chemnitz, Germany, where he got his habilitation in 1984. His field of specialization includes analysis and numerical methods for operator equations, in particular integral equations. Giuseppe Mastroianni is emeritus professor at the University of Basilicata (Italy) since 2013, where he had been full professor of Numerical Analysis since 1987. In 1971 he graduated in Mathematics at the University of Naples ""Federico II"", where he began his academic career. He is author of numerous papers on polynomial approximation, positive operators, mechanical quadrature and numerical treatment of integral equations as well as of the monographs ""Interpolation processes. Basic theory and applications"" (with G.V. Milovanovic) and ""Elementi di teoria dell'approssimazione polinomiale"" (with M.C. De Bonis and I. Notarangelo). Incoronata Notarangelo is assistant professor of Numerical Analysis at the University of Turin (Italy) since 2019. In 2010 she received a PhD in Mathematics from the University of Basilicata (Italy), in cooperation with the University of Szeged (Hungary). She is author of papers on polynomial approximation, quadrature rules and numerical methods for integral equations as well as of the monograph ""Elementi di teoria dell'approssimazione polinomiale"" (with M.C. De Bonis and G. Mastroianni).

Reviews for Weighted Polynomial Approximation and Numerical Methods for Integral Equations

“It is worthy to highlight the good structure of the book. On the one hand, the book is self-contained so deeply recommended for academic purposes and on the other hand, it is of unbounded interest for many researchers in applied and pure mathematics. Moreover, the book which are very helpful for readers. Finally, the authors also provide lists of exercises in every single chapter, very helpful also for the right understanding of the contents given.” (Eduardo Cuesta, zbMATH 1533.65004, 2024)