Generalized Locally Toeplitz Sequences: Theory and Applications: Volume I
暫譯: 廣義局部托普利茲序列：理論與應用：第一卷

Garoni, Carlo, Serra-Capizzano, Stefano

Generalized Locally Toeplitz Sequences: Theory and Applications: Volume I
  • 出版商: Springer
  • 出版日期: 2018-08-01
  • 售價: $5,330
  • 貴賓價: 9.5 折 $5,064
  • 語言: 英文
  • 頁數: 312
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3319852140
  • ISBN-13: 9783319852140

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商品描述

Based on their research experience, the authors propose a reference textbook in two volumes on the theory of generalized locally Toeplitz sequences and their applications. This first volume focuses on the univariate version of the theory and the related applications in the unidimensional setting, while the second volume, which addresses the multivariate case, is mainly devoted to concrete PDE applications.

This book systematically develops the theory of generalized locally Toeplitz (GLT) sequences and presents some of its main applications, with a particular focus on the numerical discretization of differential equations (DEs). It is the first book to address the relatively new field of GLT sequences, which occur in numerous scientific applications and are especially dominant in the context of DE discretizations. Written for applied mathematicians, engineers, physicists, and scientists who (perhaps unknowingly) encounter GLT sequences in their research, it is also of interest to those working in the fields of Fourier and functional analysis, spectral analysis of DE discretization matrices, matrix analysis, measure and operator theory, numerical analysis and linear algebra. Further, it can be used as a textbook for a graduate or advanced undergraduate course in numerical analysis.

商品描述(中文翻譯)

根據他們的研究經驗，作者提出了一本兩卷本的參考教科書，內容關於廣義局部Toeplitz序列的理論及其應用。第一卷專注於該理論的單變量版本及其在一維環境中的相關應用，而第二卷則針對多變量情況，主要致力於具體的偏微分方程（PDE）應用。

本書系統地發展了廣義局部Toeplitz（GLT）序列的理論，並介紹了一些主要應用，特別關注於微分方程（DE）的數值離散化。這是第一本探討相對較新領域GLT序列的書籍，該序列在眾多科學應用中出現，並在DE離散化的背景下尤其佔主導地位。本書是為應用數學家、工程師、物理學家和科學家撰寫的，他們在研究中（或許不自覺地）遇到GLT序列，對於從事傅立葉分析、泛函分析、DE離散化矩陣的譜分析、矩陣分析、測度與算子理論、數值分析和線性代數等領域的研究者也具有興趣。此外，本書可作為數值分析的研究生或高年級本科課程的教科書。

作者簡介

Dr. Carlo Garoni graduated in mathematics at the University of Insubria (Italy) in 2011 and received his Ph.D. in mathematics at the same university in 2015. He has pursued research at the Universities of Insubria and Rome "Tor Vergata", and he has now a Marie-Curie postdoctoral position at the USI University of Lugano (Switzerland). He has published around 20 research papers in different areas of mathematics, most of which are connected with the theory of GLT sequences and its applications.

Prof. Stefano Serra-Capizzano is full professor in numerical analysis at the University of Insubria (Italy), head of the Department of Science and High Technology at the same university, and long-term visiting professor at the Department of Information Technology at Uppsala University (Sweden). He has authored over 170 research papers in different areas of mathematics, with more than 70 collaborators all over the world. He is the founder of the Ph.D. Program "Mathematics of Computation" at the University of Insubria.

作者簡介(中文翻譯)

卡洛·加羅尼博士於2011年在意大利因蘇布里亞大學獲得數學學位，並於2015年在同一所大學獲得數學博士學位。他曾在因蘇布里亞大學和羅馬“托爾維爾加塔”大學進行研究，目前在瑞士盧加諾的美國國際大學（USI）擔任瑪麗·居里博士後職位。他在數學的不同領域發表了約20篇研究論文，其中大多數與GLT序列理論及其應用有關。

斯特凡諾·塞拉-卡皮扎諾教授是意大利因蘇布里亞大學的數值分析全職教授，該大學科學與高科技系的主任，並且是瑞典烏普薩拉大學資訊技術系的長期訪問教授。他在數學的不同領域發表了超過170篇研究論文，並與全球超過70位合作者合作。他是因蘇布里亞大學“計算數學”博士課程的創始人。

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