Open access peer-reviewed Edited Volume

Inverse Problems - Recent Advances and Applications

Ivan Kyrchei

National Academy of Sciences of Ukraine

A Leading Researcher of Pidstryhach Institute for Applied Problems in Mechanics and Mathematics of NAS, Ukraine. Dr. Kyrchei is an Editorial Board Member of the Journal ‘’Advances in Linear Algebra & Matrix Theory’’ and is a member of the International Linear Algebra Society.

Covering

Generalized Inverse Matrix Singular Value Decomposition Quaternion Matrix Tenzor Pseudoinverse Solution Matrix Equation Matrix Minimization Problem Linear Operator Equation Regularization Method Tomographic Method Iterative Reconstruction Method Convolution

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About the book

An inverse problem, which starts with the causes and then calculates the effects, covers many fields of science. In many cases, models of given inverse problems can be linearized which allows the use of methods of linear algebra for their solutions. Effective tools of linear algebra in linear inverse problems are, in particular, generalized inverse matrices as one of the ways to represent (pseudo)solutions to singular (differential) matrix equations. Nowadays, the theory of generalized inverses is one of the hot topics of linear algebra in various aspects, such as elements of the ring, operators of Hilbert space, or matrices with real, complex, and quaternion entries. Matrices over quaternion algebra are also useful tools in a lot of applied inverse problems, among them in signal and color image processing, quantum physics, etc. In recent years, methods of simultaneous decompositions for tensors have been actively used in different inverse problems. In particular, a product singular value decomposition of a quaternion tensor triplet (higher-order PSVD) has various applications in digital watermarking technology. The main goals of this book are both to give the last achievements in various areas of linear algebra, such as generalized inverses and their applications in solving matrix equations and matrix minimization problems, decompositions of matrices and tensors, new developments in theories of quaternion matrices, and operators of Hilbert space, etc. It is also important to consider new applying models of inverse problems that can be linearized.

Publishing process

Book initiated and editor appointed

Date completed: April 26th 2022

Applications to edit the book are assessed and a suitable editor is selected, at which point the process begins.

Chapter proposals submitted and reviewed

Deadline for chapter proposals: May 24th 2022

Potential authors submit chapter proposals ready for review by the academic editor and our publishing review team.

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Approved chapters written in full and submitted

Deadline for full chapters: July 23rd 2022

Once approved by the academic editor and publishing review team, chapters are written and submitted according to pre-agreed parameters

Full chapters peer reviewed

Review results due: October 11th 2022

Full chapter manuscripts are screened for plagiarism and undergo a Main Editor Peer Review. Results are sent to authors within 30 days of submission, with suggestions for rounds of revisions.

Book compiled, published and promoted

Expected publication date: December 10th 2022

All chapters are copy-checked and typesetted before being published. IntechOpen regularly submits its books to major databases for evaluation and coverage, including the Clarivate Analytics Book Citation Index in the Web of ScienceTM Core Collection. Other discipline-specific databases are also targeted, such as Web of Science's BIOSIS Previews.

About the editor

Ivan Kyrchei

National Academy of Sciences of Ukraine

Ivan Kyrchei was born in 1964 in Lviv region, Ukraine. In 1992, he was awarded a Master of Science in Mathematics from Ivan Franko National University (Lviv, Ukraine). After that, he worked a high school teacher, studied in graduate school of Pidstryhach Institute for Applied Problems in Mechanics and Mathematics of NAS of Ukraine in Lviv and started his jobs in this institute in junior research positions. In 2008, he held a Doctor of Philosophy (Candidate of Science) degree from Taras Shevchenko National University of Kyiv in specialty of Algebra and the Theory of Numbers. His PhD thesis "Theory of the column and row determinants and inverse matrix over a skew field with involution" introduces and develops the theory of new column and row determinants for matrices with noncommutative entries. In 2021, he was awarded a Doctor of Physical and Mathematical Sciences degree from Institute of Mathematics of NAS of Ukraine in Kyiv. His habilitation ScD thesis " Generalized inverse matrices over the quaternion skew field and their applications" is devoted to generalized inverse matrices over the quaternion skew field, first of all to their determinantal representations, and their applications to solving quaternion matrix equations, some differential matrix equations, and problems of quaternion matrix minimizations and approximations. Now, he is working as the Leading Researcher of PIAPMM of NAS of Ukraine. In 2014, he held an academic degree of Senior Research Fellow (Algebra and the Theory of Numbers) from Ministry of Education and Science of Ukraine that is equivalent to Associate Professor. He obtained the award for significant achievements in the field of science from the Lviv Regional State Administration and Regional Council (2019, 2021). His research interests are mostly in Algebra, Linear Algebra and their Applications. He has more than 80 scientific publications, from them more than 60 are papers with the high science citation index that have been published in well-known professional scientific journals and editor's books. He serves also as Editorial Board Member and reviewer in several SCI-journals.

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