Description

Book Synopsis
This concise introduction covers inverse problems and data assimilation, before exploring their inter-relations. Suitable for both classroom teaching and self-guided study, it is aimed at advanced undergraduates and beginning graduate students in mathematical sciences, together with researchers in science and engineering.

Table of Contents
Introduction; Part I. Inverse Problems: 1. Bayesian inverse problems and well-posedness; 2. The linear-Gaussian setting; 3. Optimization perspective; 4. Gaussian approximation; 5. Monte Carlo sampling and importance sampling; 6. Markov chain Monte Carlo; Exercises for Part I; Part II. Data Assimilation: 7. Filtering and smoothing problems and well-posedness; 8. The Kalman filter and smoother; 9. Optimization for filtering and smoothing: 3DVAR and 4DVAR; 10. The extended and ensemble Kalman filters; 11. Particle filter; 12. Optimal particle filter; Exercises for Part II; Part III. Kalman Inversion: 13. Blending inverse problems and data assimilation; References; Index.

Inverse Problems and Data Assimilation

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    A Paperback by Andrew Stuart, Andrew Stuart, Armeen Taeb

    £999.99

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      Book details

      Publisher Cambridge University Press
      Published 8 October 2023
      ISBN-13 9781009414296
      978-1009414296
      ISBN-10 1009414291
      Also in:
      Computing Applied computing Dictionaries, Reference & Language Data science and analysis Mathematics Numerical analysis

      Description

      Book Synopsis
      This concise introduction covers inverse problems and data assimilation, before exploring their inter-relations. Suitable for both classroom teaching and self-guided study, it is aimed at advanced undergraduates and beginning graduate students in mathematical sciences, together with researchers in science and engineering.

      Table of Contents
      Introduction; Part I. Inverse Problems: 1. Bayesian inverse problems and well-posedness; 2. The linear-Gaussian setting; 3. Optimization perspective; 4. Gaussian approximation; 5. Monte Carlo sampling and importance sampling; 6. Markov chain Monte Carlo; Exercises for Part I; Part II. Data Assimilation: 7. Filtering and smoothing problems and well-posedness; 8. The Kalman filter and smoother; 9. Optimization for filtering and smoothing: 3DVAR and 4DVAR; 10. The extended and ensemble Kalman filters; 11. Particle filter; 12. Optimal particle filter; Exercises for Part II; Part III. Kalman Inversion: 13. Blending inverse problems and data assimilation; References; Index.

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