Advances in Numerical Analysis Emphasizing Interval Data

Tofigh Allahviranloo, Witold Pedrycz, Armin Esfandiari

• Publisher: CRC Press
• Year: 2022
• Print ISBN: 9781032110431
• eBook ISBN: 9781000540314
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

Numerical analysis forms a cornerstone of numeric computing and optimization, in particular recently, interval numerical computations play an important role in these topics. The interest of researchers in computations involving uncertain data, namely interval data opens new avenues in coping with real-world problems and deliver innovative and efficient solutions. This book provides the basic theoretical foundations of numerical methods, discusses key technique classes, explains improvements and improvements, and provides insights into recent developments and challenges.

The theoretical parts of numerical methods, including the concept of interval approximation theory, are introduced and explained in detail. In general, the key features of the book include an up-to-date and focused treatise on error analysis in calculations, in particular the comprehensive and systematic treatment of error propagation mechanisms, considerations on the quality of data involved in numerical calculations, and a thorough discussion of interval approximation theory.

Moreover, this book focuses on approximation theory and its development from the perspective of linear algebra, and new and regular representations of numerical integration and their solutions are enhanced by error analysis as well. The book is unique in the sense that its content and organization will cater to several audiences, in particular graduate students, researchers, and practitioners.

1 About the Book

DOI: 10.1201/9781003218173-1

Numerical analysis forms a cornerstone of numeric computing and optimization, in particular recently, interval numerical computations play an important role in these topics. The interest of researchers in computations involving uncertain data, namely, interval data, opens new avenues in coping with real-world problems and delivers innovative and efficient solutions.

The book delivers essential theoretical fundamentals of numerical methods, discusses classes of key techniques, elaborates on their refinements and enhancements, and offers insights into the recent developments and existing challenges.

The theoretical parts of numerical methods including the concept of interval approximation theory are introduced and explained in detail. In general, the key features of the book include:

• Updated and focused treatise on error analysis in computing, especially a comprehensive and systematic treatment of mechanisms of error propagation.
• Considerations on quality of data involved in numeric computing with a thorough discussion of interval approximation theory.
• Focus on approximation theory and its development from the linear algebra point of view.
• A new and well-organized exposure of numerical integration and their solutions enhanced with error analysis.

2 Error Analysis

DOI: 10.1201/9781003218173-2

2.1 Introduction

Based on the discussed numerical methods and considering other chapters of the book, we need to explain the error analysis first. In addition to exploring the numerical integration methods, the interpolation of integrand function is needed and this is one of the reasons to discuss about interpolation methods.

2.2 Error Analysis

In this chapter, we intend to investigate and analyze the important complicated problems and points that occur in numerical calculations or calculations based on the numerical algorithms. As we know, in the numerical analysis, most numerical methods ar...

Table of contents

• Cover
• Half Title Page
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Authors
• 1 About the Book
• 2 Error Analysis
• 3 Interpolation
• 4 Advanced Interpolation
• 5 Interval Interpolation
• 6 Interpolation from the Linear Algebra Point of View
• 7 Newton-Cotes Quadrature
• 8 Interval Newton-Cotes Quadrature
• 9 Gauss Integration
• Index