Problems where SPD linear system arises

Question

I know some of the places where SPD linar systems arises such as elliptic PDEs and normal equations. Can I have a more comprehensive list of scientific applications which require solving SPD linear system. I am specially interested in cases where matrix is not sparse

Thanks

Answer 1

One place, where symmetric positive definite linear systems often arise, is in the field of statistics. The covariance matrix is, by definition, symmetric and positive definite. In general, this is dense, though people sparsify it to make it computationally friendly.

Dense covariance matrices are often used in Bayesian inference, inverse modelling, etc.