Efficient implementations of the SOLA mollifier method

Abstract

We describe efficient implementations of the Subtractive Optimally Localized Averages (SOLA) mollifier method for solving linear inverse problems in, e.g., inverse helioseismology. We show that the SOLA method can be regarded as a constrained least squares problem, which can be solved by means of standard "building blocks" from numerical linear algebra. We compare the standard implementation of the SOLA algorithm with our new approaches based on bidiagonalization of the kernel matrix, which allow fast re-computation of the solution when the regularization parameter or the target function are changed. We also illustrate our methods with an example from helioseismology.