{"title":"Inverse Problems","authors":"Kazufumi Ito, Bangti Jin","doi":"10.1142/9120","DOIUrl":"https://doi.org/10.1142/9120","url":null,"abstract":"Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference.The book offers a comprehensive treatment of modern techniques, and seamlessly blends regularization theory with computational methods, which is essential for developing accurate and efficient inversion algorithms for many practical inverse problems.It demonstrates many current developments in the field of computational inversion, such as value function calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton method, direct sampling method, uncertainty quantification and approximate Bayesian inference. It is written for graduate students and researchers in mathematics, natural science and engineering.","PeriodicalId":407331,"journal":{"name":"Series on Applied Mathematics","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123312938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Ordinary Differential Equations with Applications","authors":"S. Hsu","doi":"10.1142/8744","DOIUrl":"https://doi.org/10.1142/8744","url":null,"abstract":"Fundamental Theory Linear Systems Stability of Nonlinear Systems Method of Lyapunov Functions Two-Dimensional Systems Second Order Linear Equations The Index Theory and Brouwer Degree Monotone Dynamical Systems Introduction to Perturbation Methods.","PeriodicalId":407331,"journal":{"name":"Series on Applied Mathematics","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121529591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Machine proofs in geometry - automated production of readable proofs for geometry theorems","authors":"S. Chou, Xiao Gao, Jing-Zhong Zhang","doi":"10.1142/2196","DOIUrl":"https://doi.org/10.1142/2196","url":null,"abstract":"The Hilbert intersection point theorems the constructive theorems the Hilbert intersection point theorems in solid geometry a collection of theorems and proofs automatically generated by computers.","PeriodicalId":407331,"journal":{"name":"Series on Applied Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121515454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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