Which algorithm you would recommend for fast solution of dense linear system of fixed dimension (N=9) (matrix is symmetric, positive-semidefinite)?
Because of its ease of use, you can take Eigen solvers just for comparison. For specific use case a specific solver might be faster although another is supposed to be better. For that, you can measure runtimes for the each algorithm just for the selection. After that you can implement the desired option (or find an existing one that fits your needs the best).