A theory for optimal regularization in the finite dimensional case |
| |
Authors: | John W. Hilgers |
| |
Affiliation: | Department of Mathematical and Computer Sciences Michigan Technological University Houghton, Michigan 49931 USA |
| |
Abstract: | Consider the matrix problem in the case where A is known precisely, the problem is ill conditioned, and ε is a random noise vector. Compute regularized “ridge” estimates,,where 1 denotes matrix transpose. Of great concern is the determination of the value of λ for which x?λ “best” approximates . Let ,and define λ0 to be the value of λ for which Q is a minimum. We look for λ0 among solutions of dQ/dλ = 0. Though Q is not computable (since ε is unknown), we can use this approach to study the behavior of λ0 as a function of y and ε. Theorems involving “noise to signal ratios” determine when λ0 exists and define the cases λ0 > 0 and λ0 = ∞. Estimates for λ0 and the minimum square error Q0 = Q(λ0) are derived. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|