[ { "id": "https://authors.library.caltech.edu/records/mf2kc-m5915", "eprint_id": 71920, "eprint_status": "archive", "datestamp": "2023-08-20 02:30:13", "lastmod": "2023-10-23 17:41:04", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Stuart-A-M", "name": { "family": "Stuart", "given": "Andrew" } }, { "id": "Voss-J", "name": { "family": "Voss", "given": "Jochen" }, "orcid": "0000-0001-7740-8811" } ] }, "title": "Matrix Analysis and Algorithms", "ispublished": "unpub", "full_text_status": "public", "note": "
Submitted - numlinalg.pdf
", "abstract": "The book contains an introduction to matrix analysis, and to the basic algorithms of numerical linear algebra. Further results can be found in many text books. The book of Horn and Johnson [HJ85] is an excellent reference for theoretical results about matrix analysis; see also\n[Bha97]. The subject of linear algebra, and matrix analysis in particular, is treated in an original and illuminating fashion in [Lax97]. For a general introduction to the subject of numerical linear algebra we recommend the book by Trefethen and Bau [TB97]; more theoretical treatments of\nthe subject can be found in Demmel [Dem97], Golub and Van Loan [GL96] and in Stoer and Bulirsch [SB02]. Higham's book [Hig02] contains a wealth of information about stability and\nthe effect of rounding errors in numerical algorithms; it is this source that we used for almost all theorems we state concerning backward error analysis. The book of Saad [Saa97] covers the subject of iterative methods for linear systems. The symmetric eigenvalue problem is analysed\nin Parlett [Par80].", "date": "2016-11-15", "date_type": "published", "publisher": "Caltech Library", "id_number": "CaltechAUTHORS:20161110-160355297", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-160355297", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "primary_object": { "basename": "numlinalg.pdf", "url": "https://authors.library.caltech.edu/records/mf2kc-m5915/files/numlinalg.pdf" }, "resource_type": "book", "pub_year": "2016", "author_list": "Stuart, Andrew and Voss, Jochen" }, { "id": "https://authors.library.caltech.edu/records/5b3bk-adp93", "eprint_id": 71922, "eprint_status": "archive", "datestamp": "2023-08-20 04:16:16", "lastmod": "2024-01-13 20:19:19", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Law-K-J-H", "name": { "family": "Law", "given": "Kody" } }, { "id": "Stuart-A-M", "name": { "family": "Stuart", "given": "Andrew" } }, { "id": "Zygalakis-K-C", "name": { "family": "Zygalakis", "given": "Konstantinos" } } ] }, "title": "Data Assimilation: A Mathematical Introduction", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2015 Sprinter International Publishing Switzerland.\n\nSome of the research described in the book has emerged from collaborations with others, and the authors are indebted to all of their coauthors on collaborative work cited in the bibliography sections. The authors are very grateful to Sergios Agapiou, Daniel Sanz-Alonso, and Yuan-Xiang Zhang for help in typesetting parts of this book, and for input regarding the presentation; furthermore, Ian Hawke and Gregory Ashton provided help with the preparation of the figures, while Daniel Sanz-Alonso road-tested many of the exercises. The authors also wish to thank Mel Ades and H\u00e5kon Hoel for useful feedback, which helped to improve the presentation. The anonymous reviewers chosen by Springer and editors at Springer also gave very useful feedback, and Achi Dosanjh from Springer provided very helpful overall guidance and support throughout the publication process. And finally,\nthe authors thank the student audiences at Peking University (2012), KAUST (2014), the University of Warwick (2014), and Fudan University (2015), whose interest helped to shape\nthe notes. AMS is grateful to EPSRC, ERC, ESA, and ONR for financial support for research whose development suggested the need for a mathematization of the subject of data assimilation. KJHL was supported as a member of the SRI-UQ Center at KAUST while much of the writing of this book was undertaken.\n\nSubmitted - 1506.07825.pdf
", "abstract": "This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online.\n\nThe book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters.\n\nThis book is aimed at mathematical researchers interested in a systematic development of this interdisciplinary field, and at researchers from the geosciences, and a variety of other scientific fields, who use tools from data assimilation to combine data with time-dependent models. The numerous examples and illustrations make understanding of the theoretical underpinnings of data assimilation accessible. Furthermore, the examples, exercises and MATLAB software, make the book suitable for students in applied mathematics, either through a lecture course, or through self-study.", "date": "2015", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham, Switerland", "id_number": "CaltechAUTHORS:20161110-161028249", "isbn": "978-3-319-20325-6", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-161028249", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Engineering and Physical Sciences Research Council (EPSRC)" }, { "agency": "European Research Council (ERC)" }, { "agency": "European Space Agency (ESA)" }, { "agency": "Office of Naval Research (ONR)" } ] }, "other_numbering_system": { "items": [ { "id": "B4", "name": "Andrew Stuart" } ] }, "doi": "10.1007/978-3-319-20325-6", "primary_object": { "basename": "1506.07825.pdf", "url": "https://authors.library.caltech.edu/records/5b3bk-adp93/files/1506.07825.pdf" }, "resource_type": "book", "pub_year": "2015", "author_list": "Law, Kody; Stuart, Andrew; et el." }, { "id": "https://authors.library.caltech.edu/records/qr46p-gdt32", "eprint_id": 71924, "eprint_status": "archive", "datestamp": "2023-08-19 22:05:53", "lastmod": "2024-01-13 20:19:22", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gonzalez-O", "name": { "family": "Gonzalez", "given": "Oscar" } }, { "id": "Stuart-A-M", "name": { "family": "Stuart", "given": "Andrew M." } } ] }, "title": "A First Course in Continuum Mechanics", "ispublished": "unpub", "full_text_status": "public", "keywords": "Fluid Dynamics and Solid Mechanics, Engineering, Mathematical Physics, Solid Mechanics and Materials, Differential and Integral Equations, Dynamical Systems and Control Theory, Mathematics", "note": "\u00a9 2008 Cambridge University Press.", "abstract": "A concise account of various classic theories of fluids and solids, this book is for courses in continuum mechanics for graduate students and advanced undergraduates. Thoroughly class-tested in courses at Stanford University and the University of Warwick, it is suitable for both applied mathematicians and engineers. The only prerequisites are an introductory undergraduate knowledge of basic linear algebra and differential equations. Unlike most existing works at this level, this book covers both isothermal and thermal theories. The theories are derived in a unified manner from the fundamental balance laws of continuum mechanics. Intended both for classroom use and for self-study, each chapter contains a wealth of exercises, with fully worked solutions to odd-numbered questions. A complete solutions manual is available to instructors upon request. Short bibliographies appear at the end of each chapter, pointing to material which underpins or expands upon the material discussed.", "date": "2008-02", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge, UK", "id_number": "CaltechAUTHORS:20161110-163303162", "isbn": "9780521714242", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-163303162", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "B2", "name": "Andrew Stuart" } ] }, "doi": "10.1017/CBO9780511619571", "resource_type": "book", "pub_year": "2008", "author_list": "Gonzalez, Oscar and Stuart, Andrew M." }, { "id": "https://authors.library.caltech.edu/records/q2sa8-wy532", "eprint_id": 71923, "eprint_status": "archive", "datestamp": "2023-08-19 21:52:58", "lastmod": "2024-01-13 20:19:20", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Pavliotis-G-A", "name": { "family": "Pavliotis", "given": "Grigorios A." } }, { "id": "Stuart-A-M", "name": { "family": "Stuart", "given": "Andrew M." } } ] }, "title": "Multiscale Methods: Averaging and Homogenization", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2008 Springer.\n\nGP has received financial support from the EPSRC, and AMS has received financial support from the EPSRC and from the U.S. Office of Naval Research during the writing of this book. This funded research has helped shape much of the material\npresented in the book, and the authors are grateful for the financial support.", "abstract": "This introduction to multiscale methods gives readers a broad overview of the many uses and applications of the methods. The book begins by setting the theoretical foundations of the subject area, and moves on to develop a unified approach to the simplification of a wide range of problems which possess multiple scales, via perturbation expansions; differential equations and stochastic processes are studied in one unified framework. The book concludes with an overview of a range of theoretical tools used to justify the simplified models derived via the perturbation expansions.\n\nThe presentation of the material is particularly suited to the range of mathematicians, scientists and engineers who want to exploit multiscale methods in applications. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable readers to build their own skills and put them into practice.\n\nExtensions and generalizations of the results presented in the book, as well as references to the literature, are provided in the Discussion and Bibliography section at the end of each chapter. All of the twenty-one chapters are supplemented with exercises.", "date": "2008", "date_type": "published", "publisher": "Springer", "place_of_pub": "New York", "id_number": "CaltechAUTHORS:20161110-162102417", "isbn": "978-0-387-73829-1", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-162102417", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Engineering and Physical Sciences Research Council (EPSRC)" }, { "agency": "Office of Naval Research (ONR)" } ] }, "other_numbering_system": { "items": [ { "id": "B3", "name": "Andrew Stuart" } ] }, "doi": "10.1007/978-0-387-73829-1", "resource_type": "book", "pub_year": "2008", "author_list": "Pavliotis, Grigorios A. and Stuart, Andrew M." }, { "id": "https://authors.library.caltech.edu/records/5w6jy-4k716", "eprint_id": 71925, "eprint_status": "archive", "datestamp": "2023-08-20 06:59:48", "lastmod": "2024-03-05 18:28:47", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Stuart-A-M", "name": { "family": "Stuart", "given": "A. M." }, "orcid": "0000-0001-9091-7266" }, { "id": "Humphries-A-R", "name": { "family": "Humphries", "given": "A. R." } } ] }, "title": "Dynamical Systems and Numerical Analysis", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1998 Cambridge University Press.", "abstract": "This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulted as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strage attractors under numerical approximation. This book will be an invaluable tool for graduate students and researchers in the fields of numerical analysis and dynamical systems.", "date": "1996", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge, UK", "id_number": "CaltechAUTHORS:20161110-163922626", "isbn": "9780521645638", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-163922626", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "collection": "CaltechAUTHORS", "other_numbering_system": { "items": [ { "id": "B1", "name": "Andrew Stuart" } ] }, "resource_type": "book", "pub_year": "1996", "author_list": "Stuart, A. M. and Humphries, A. R." } ]