Minimization of functionals on the solution of a large-scale discrete ill-posed problem

作者：Martin David R; Reichel Lothar^*

来源：BIT Numerical Mathematics, 2013, 53(1): 153-173.

DOI：10.1007/s10543-012-0396-y

• Ill-posed problem
• Trust region
• Quadrature
• Confidence intervals

In this work we study the minimization of a linear functional defined on a set of approximate solutions of a discrete ill-posed problem. The primary application of interest is the computation of confidence intervals for components of the solution of such a problem. We exploit the technique introduced by Eld,n in 1990, utilizing a parametric programming reformulation involving the solution of a sequence of quadratically constrained least squares problems. Our iterative method, which uses the connection between Lanczos bidiagonalization and Gauss-type quadrature rules to bound certain matrix functionals, is well-suited for large-scale problems, and offers a significant reduction in matrix-vector product evaluations relative to available methods.

• 出版日期2013-3