Inverse Problems, Regularization Methods and Related Topics

This book features a thoughtfully curated collection of research contributions spanning regularization theory, integral equations, learning theory, and matrix and operator theory. These contributions were presented in honor of Prof. M. Thamban Nair on his 65th birthday during the International Conference on Analysis, Inverse Problems, and Applications, which took place at the IIT Madras in Chennai, India, from July 1821, 2022. The book is a valuable resource for graduate students, engineers, scientists, and researchers looking to advance their work in the development of innovative regularization algorithms. It comprises 14 chapters contributed by esteemed experts and emerging researchers.

Presents recent research on computational mathematics, functional analysis, and mathematical modeling Emphasizes the role of the regularization theory in the design of stable algorithms for real-life problems Features research papers in regularization theory, integral equations, learning theory, and matrix and operator theory

Autorentext

Sergei V. Pereverzyev is a professor and senior fellow of the Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Wien, Austria. He is the second recipient of the International Prize for Achievement in Information-Based Complexity (2000) and the inventor of a patented innovation in diabetes technology (2019). He is an author of 3 books and more than 100 scholarly articles. He serves as a member of editorial boards of several international journals: Applied and Computational Harmonic Analysis, Journal of Complexity, Computational Methods in Applied Mathematics, Numerical Functional Analysis and Optimization, International Journal on Geomathematics, Frontiers in Applied Mathematics and Statistics, International Journal of Wavelets, Multiresolution and Information Processing and Ukrainian Mathematical Journal.

Radha Ramakrishnan is a senior professor in the Department of Mathematics, Indian Institute of Technology (IIT) Madras, Chennai, India. With more than 25 years of teaching and research experience, she has guided several Ph.D. students and postdoctoral researchers who at present are working at different IITs. She has published more than 60 research papers in international journals and edited 3 international conference proceedings. She is also serving as a member of editorial board for journals: Mathematics of Computation and Data Science, Frontiers in Applied Mathematics and Statistics and Sampling Theory, Signal Processing, and Data Analysis.

Sivananthan Sampath is a professor in the Department of Mathematics, Indian Institute of Technology (IIT) Delhi, New Delhi, India. Having obtained his Ph.D. from the IIT Madras in 2008, before joining the IIT Delhi in 2012, he pursued postdoctoral research at Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Austria. In recognition of his teaching abilities, he received a teaching excellence award from the IIT Delhi and is also one of the inventors of a patented innovation in diabetes technology (2019). He has co-authored more than 25 scholarly articles and serves as a member of the editorial board for the Sampling Theory, Signal Processing, and Data Analysis journal.

Inhalt

Chapter 1 A Class of Frozen Regularized GaussNewton Methods under Weak Conditions.- Chapter 2 Projection-based Approximations of Integral Equation of the First Kind.- Chapter 3 Approximate Solution of Fredholm Integral Equations of the Second Kind.