EFFICIENT IMPLEMENTATIONS OF THE SOLA MOLLIFIER METHOD

We describe efficient implementations of the Subtractive Optimally Loc alized Averages (SOLA) mollifier method for solving linear inverse pro blems in, e.g., inverse helioseismology. We show that the SOLA method can be regarded as a constrained least squares problem, which can be s olved by means of standard ''building blocks'' from numerical linear a lgebra. We compare the standard implementation of the SOLA algorithm w ith our new approaches based on bidiagonalization of the kernel matrix , which allow fast re-computation of the solution when the regularizat ion parameter or the target function are changed. We also illustrate o ur methods with an example from helioseismology.