An iterative algorithm for solving ill-conditioned linear least squares problems
نویسندگان
چکیده
منابع مشابه
Preconditioned Iterative Methods for Solving Linear Least Squares Problems
New preconditioning strategies for solving m × n overdetermined large and sparse linear least squares problems using the CGLS method are described. First, direct preconditioning of the normal equations by the Balanced Incomplete Factorization (BIF) for symmetric and positive definite matrices is studied and a new breakdown-free strategy is proposed. Preconditioning based on the incomplete LU fa...
متن کاملRegularization of Large-scale Ill-conditioned Least Squares Problems Regularization of Large{scale Ill{conditioned Least Squares Problems
Ill{conditioned problems arise in important areas like geophysics, medical imaging and signal processing. The fact that the ill{cond-itioning is an intrinsic feature of these problems makes it necessary to develop special numerical methods to treat them. Regularization methods belong to this class. The lack of robust regularization methods for large{scale ill{cond-itioned problems motivated thi...
متن کاملLeast-squares Polynomial Lters for Ill-conditioned Linear Systems
An important problem which arises in several applications is to nd the solution of an ill-conditioned Symmetric Semi-Positive Deenite linear system whose right-hand side is perturbed by noise. In this situation, it is desirable for the solution to be accurate in the directions of eigenvectors associated with large eigenvalues, and to have small components in the space associated with smallest e...
متن کاملLSMR: An iterative algorithm for sparse least-squares problems
An iterative method LSMR is presented for solving linear systems Ax = b and leastsquares problems min ‖Ax−b‖2, with A being sparse or a fast linear operator. LSMR is based on the Golub-Kahan bidiagonalization process. It is analytically equivalent to the MINRES method applied to the normal equation ATAx = ATb, so that the quantities ‖Ark‖ are monotonically decreasing (where rk = b−Axk is the re...
متن کاملAn Algorithm for Solving Scaled Total Least Squares Problems
In this paper, we present a rankrevealing two-sided orthogonal decomposition method for solving the STLS problem. An error analysis of the algorithm is given. Our numerical experiments show that this algorithm computes the STLS solution as accurate as the SVD method with less computation.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Geodesy and Geodynamics
سال: 2015
ISSN: 1674-9847
DOI: 10.1016/j.geog.2015.06.004