I know that compact self-adjoint operators have a countable, orthonornal eigendecomposition, and the spectrum is real and positive, and the only cluster point is zero.
What sorts of algorithms does one use to compute the first K eigenvalues of a compact self-adjoint operator? Is it similar to computing the eigenvalues for a symmetric matrix (like these algorithms)? I know that symmetric matrices and compact self-adjoint operators are analogous in some ways.