Subject: QA | Stokes flow | Bayesian | Inverse problem | 65P99 | Mathematics - Probability | Numerical Analysis | 65C05 | Data assimilation | Markov chain-Monte Carlo | /dk/atira/pure/subjectarea/asjc/2600/2612 | Mathematics - Numerical Analysis
Inverse problems are often ill posed, with solutions that depend sensitively on data.n any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability. This paper is based on an approach to regulariz... View more
 A. Apte, C. K. R. T. Jones, A. M. Stuart, and J. Voss, Data assimilation: Mathematical and statistical perspectives, Internat. J. Numer. Methods Fluids, 56 (2008), pp. 1033-1046.
 S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, and T. Tarvainen, Approximation errors and model reduction with an application to optical diffusion tomography, Inverse Problems, 22 (2006), pp. 175-195.
 V. I. Bogachev, Gaussian Measures, American Mathematical Society, Providence, RI, 1998.
 D. Calvetti and E. Somersalo, Introduction to bayesian scientific computing, Surveys and Tutorials in the Applied Mathematical Sciences 2, Springer, New York, 2007.
 S. L. Cotter, M. Dashti, J. C. Robinson, and A. M. Stuart, Bayesian inverse problems for functions and applications to fluid mechanics, Inverse Problems, 25 (2010), p. 115008.
 S. L. Cotter, M. Dashti, J. C. Robinson, and A. M. Stuart, MCMC Methods on Function Space and Applications to Fluid Mechanics, in preparation, 2010.
 M. Dashti and J. C. Robinson, A simple proof of uniqueness of the particle trajectories for solutions of the Navier-Stokes equations, Nonlinearity, 22 (2009), pp. 735-746.
 H. K. Engl, M. Hanke, and A. Neubauer, Regularization of inverse problems, Kluwer, Dordrecht, the Netherlands, 1996.
 J. N. Franklin, Well-posed stochastic extensions of ill posed linear problems, J. Math. Anal. Appl., 31 (1970), pp. 682-716.
 A. Hofinger and H. K. Pikkarainen, Convergence rates for the Bayesian approach to linear inverse problems, Inverse Problems, 23 (2007), pp. 2469-2484.