03103nam a22004935i 4500 978-3-031-74379-5 DE-He213 20251030113308.0 cr nn 008mamaa 241112s2024 sz | s |||| 0|eng d 9783031743795 978-3-031-74379-5 10.1007/978-3-031-74379-5 doi QA1-939 PB bicssc MAT000000 bisacsh PB thema Söderlind, Gustaf. author. aut http://id.loc.gov/vocabulary/relators/aut 87377 Logarithmic Norms [electronic resource] / by Gustaf Söderlind. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIV, 493 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Series in Computational Mathematics, 2198-3712 ; 63 Part I Introduction to logarithmic norms -- Part II Matrix Theory -- Part III Nonlinear maps -- Part IV Differential Operators -- Further reading.-Bibliography -- Index. This book offers the first comprehensive account of how the logarithmic norm is used for matrices, nonlinear maps and linear differential operators, with a focus on initial and boundary value problems. Complementing the usual operator norm, the logarithmic norm is a versatile tool which provides unique additional information on the magnitude of an operator. It is instrumental in the stability theory of dynamical systems and in the theory of elliptic operator equations. The text adopts a unified approach to address a wide range of themes in applied mathematics. It explores the role of the logarithmic norm in scientific computing, compares the operator bounds with those of spectral theory, and illustrates the theory with classical models from science and engineering. Many previously unpublished results are presented alongside established material, supporting researchers in applied mathematics and computational engineering who seek a systematic approach to stability and perturbation bounds in initial value problems, boundary value problems and partial differential equations. Primarily intended as a reference text, the book can also serve as a graduate text for PhD students. Mathematics. 65523 Mathematics. 65523 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031743788 Printed edition: 9783031743801 Printed edition: 9783031743818 Springer Series in Computational Mathematics, 2198-3712 ; 63 87145 https://doi.org/10.1007/978-3-031-74379-5 ZDB-2-SMA ZDB-2-SXMS 64888 64888