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## Meet the editor

Dr. Ivan I. Kyrchei received an MSc in mathematics from Ivan Franko National University, Lviv, Ukraine in 1992, a Ph.D. from Taras Shevchenko National University, Kyiv, Ukraine in 2008, and a DSc in algebra and theory numbers from the NASU Institute of Mathematics, Kyiv in 2021. He is currently the Lead Researcher at NASU's Pidstryhach Institute for Applied Problems of Mechanics and Mathematics (IAPMM), Ukraine,

where he has worked for more than 20 years. He has published more than 100 papers in scientific journals and international conference proceedings on the theory of quaternion matrix equations, generalized inverse matrices, and functionals of matrices over quaternion algebras. He is also the editor of three books and a member of the editorial boards of five international scientific journals.

### Contents


Preface

*Inverse Problems - Recent Advances and Applications* examines new aspects of the mathematical modeling of inverse problems, their applications in physical systems, and the computational methods used. The book's five chapters are divided into two sections. Section 1, "Modeling and Formulations of Inverse Problems", discusses new approaches in the modeling and formulation of inverse problems in some physical systems. Chapter 1 formulates the initial statement of the inverse problem. Chapter 2 introduces recent applications of the Ensemble Kalman Filter to inverse problems, known as ensemble Kalman inversion. The subject of Chapter 3 is the evaluation of gradients in inverse problems where spatial field parameters and geometry

Section 2, "Some Computational Aspects", concerns mathematical methods of solving some inverse problems. Chapter 4 reviews individual solutions for the tomographic problem, including strategies for removing deficiencies of the ill-posed problem by using truncated singular value decomposition and the L-curve technique. Chapter 5 discusses the least norm of the solution to some system of quaternion matrix equations and its expression by determinantal representations (analogs of Cramer's rule) using

Pidstryhach Institute for Applied Problems of Mechanics and Mathematics,

**Ivan I. Kyrchei**

Lviv, Ukraine

National Academy of Sciences of Ukraine,

parameters are treated separately.

row-column noncommutative determinants.
