Practical optimal regularization of large linear systems
Preconditioners for least squares problems by LU factorization.
Preconditionings and Splittings for Rectangular Systems.
Quadratically constrained least squares and quadratic problems.
Regular Splittings and the Discrete Neumann Problem.
Robust quasi-linear system identification
Self-correcting iterative methods for computing -inverses
In this paper we construct a few iterative processes for computing -inverses of a linear bounded operator. These algorithms are extensions of the corresponding algorithms introduced in [11] and a method from [8]. A few error estimates are derived.
Solvability classes for core problems in matrix total least squares minimization
Linear matrix approximation problems are often solved by the total least squares minimization (TLS). Unfortunately, the TLS solution may not exist in general. The so-called core problem theory brought an insight into this effect. Moreover, it simplified the solvability analysis if is of column rank one by extracting a core problem having always a unique TLS solution. However, if the rank of is larger, the core problem may stay unsolvable in the TLS sense, as shown for the first time by Hnětynková,...
Stability of the Solutions of Linear Least Squares Problems.
Strict Chebyshev Approximation for General Systems of Linear Equations.
Strong Underrelaxation in Kaczmarz's Method for Inconsistent Systems
The anti-symmetric ortho-symmetric solutions of the matrix equation XA=D.
The descent algorithms for solving symmetric Pareto eigenvalue complementarity problem
For the symmetric Pareto Eigenvalue Complementarity Problem (EiCP), by reformulating it as a constrained optimization problem on a differentiable Rayleigh quotient function, we present a class of descent methods and prove their convergence. The main features include: using nonlinear complementarity functions (NCP functions) and Rayleigh quotient gradient as the descent direction, and determining the step size with exact linear search. In addition, these algorithms are further extended to solve the...
The Drazin inverse in multibody system dynamics.
The interplay between classical analysis and (numerical) linear algebra -- a tribute to Gene H. Golub.
The minimum-norm least-squares solution of a linear system and symmetric rank-one updates.
The Strict Chebyshev Solution of Overdetermined Systems of Linear Equations with Rank Deficient Matrix
The structured sensitivity of Vandermonde-like systems.
The symmetric minimal rank solution of the matrix equation and the optimal approximation.
Updating the Singular Value Decomposition.