27th Conference of the International Linear Algebra Society (ILAS 2026)

Discretization-free Bayesian inverse problems

May 21, 2026, 2:00 PM

25m

Torgersen Hall 1030 (Virginia Tech)

Minisymposium Talk Inverse Problems and Uncertainty Quantification through the Lens of Numerical Linear Algebra Inverse Problems and Uncertainty Quantification through the Lens of Numerical Linear Algebra

Speaker

Erkki Somersalo (Case Western Reserve University)

Description

In this talk, we revisit the Bayesian inverse problems formalism in infinite-dimensional distribution spaces, where function evaluations are replaced by evaluations by test functions. It is shown that linear inverse problems can be formulated without a reference to any infinite-dimensional representation of the unknown, e.g., in terms of basis vectors, and therefore, the forward problem has a matrix-free form. In the Gaussian case, the numerical evaluation of the posterior mean and covariance matrix does not rely on finite-dimensional approximations of the unknown, but rather on numerical quadratures. The formalism is flexible, allowing a posteriori probing of the unknown without recalculation of any matrix inverses.