A&A Supplement series, Vol 121, March 1997, 587-598

Received November 29, 1995; accepted June 20, 1996

Efficient implementations of the SOLA mollifier method

R.M. Larsen - P.C. Hansen

Send offprint request: R.M. Larsen

  Department of Computer Science, University of Aarhus, Ny Munkegade, Building 540, DK-8000 Aarhus C, Denmark
  UNIC, Danish Computing Center for Research and Education, Building 304, Technical University of Denmark, DK-2800 Lyngby, Denmark

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.

keywords: methods: numerical; analytical -- Sun: oscillations

 
• 1. Introduction
• 2. Implementations of the SOLA method
• 3. Available software
• 4. The computational efficiency of the algorithms
• 5. An example from helioseismology
• 6. Conclusion
• References