{"product_id":"hardback-9781009414326","title":"(Hardback) 9781009414326","description":"\u003cfont face=\"Georgia\"\u003e\r\n\r\n\r\n\r\n\u003cp\u003e\u003cem\u003eA clear and concise mathematical introduction to the subjects of inverse problems and data assimilation, and their inter-relations.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDaniel Sanz-Alonso (Author), Andrew Stuart (Author), Armeen Taeb (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009414326, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 31 August 2023\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e221 pages\u003cbr\u003e28 x 19 x 2 cm, 0.562 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis concise introduction provides an entry point to the world of inverse problems and data assimilation for advanced undergraduates and beginning graduate students in the mathematical sciences. It will also appeal to researchers in science and engineering who are interested in the systematic underpinnings of methodologies widely used in their disciplines. The authors examine inverse problems and data assimilation in turn, before exploring the use of data assimilation methods to solve generic inverse problems by introducing an artificial algorithmic time. Topics covered include maximum a posteriori estimation, (stochastic) gradient descent, variational Bayes, Monte Carlo, importance sampling and Markov chain Monte Carlo for inverse problems; and 3DVAR, 4DVAR, extended and ensemble Kalman filters, and particle filters for data assimilation. The book contains a wealth of examples and exercises, and can be used to accompany courses as well as for self-study.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e Part I. Inverse Problems: 1. Bayesian inverse problems and well-posedness\u003cbr\u003e 2. The linear-Gaussian setting\u003cbr\u003e 3. Optimization perspective\u003cbr\u003e 4. Gaussian approximation\u003cbr\u003e 5. Monte Carlo sampling and importance sampling\u003cbr\u003e 6. Markov chain Monte Carlo\u003cbr\u003e Exercises for Part I\u003cbr\u003e Part II. Data Assimilation: 7. Filtering and smoothing problems and well-posedness\u003cbr\u003e 8. The Kalman filter and smoother\u003cbr\u003e 9. Optimization for filtering and smoothing: 3DVAR and 4DVAR\u003cbr\u003e 10. The extended and ensemble Kalman filters\u003cbr\u003e 11. Particle filter\u003cbr\u003e 12. Optimal particle filter\u003cbr\u003e Exercises for Part II\u003cbr\u003e Part III. Kalman Inversion: 13. Blending inverse problems and data assimilation\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Numerical analysis [\u003ca title=\"See our other books on Numerical analysis\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Numerical%20analysis%20%5BPBKS%5D%22\"\u003ePBKS\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46297230344472,"sku":"9781009414326","price":59.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781009414326i.jpg?v=1692250916","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/hardback-9781009414326","provider":"Freshly Printed Books","version":"1.0","type":"link"}