Characterization of Linear Stationary Iterative Processes for Solving a Singular System of Linear Equations.
Chipman pseudoinverse of matrix, its computation and application in spline theory
Computing generalized inverse systems using matrix pencil methods
We address the numerically reliable computation of generalized inverses of rational matrices in descriptor state-space representation. We put particular emphasis on two classes of inverses: the weak generalized inverse and the Moore-Penrose pseudoinverse. By combining the underlying computational techniques, other types of inverses of rational matrices can be computed as well. The main computational ingredient to determine generalized inverses is the orthogonal reduction of the system matrix pencil...
Constrained least squares methods for linear timevarying DAE systems.
Contribuciones a la generalización del problema de compensación por grupos de Helmert-Pranis Pranievich.
The paper presents in a generalized form the problem of the geodetic network adjustment by the Helmert-Pranis Pranievich groups method (groups with junction points included or not). The adjustment problem, as well as the cofactor matrix derivation for the partial-independent and linkage unknowns, was completely formulated by transformed weight matrix definition and usage. A complete sequence of the computing stages for the geodetic networks divided into groups without junction points was given for...
Convergence of approximate splines via pseudo-inverses
Direct Error Analysis for Least Squares.
Direct iterative methods for linear systems using weak splittings
Displacement preconditioner for Toeplitz least squares iterations.
Displacement Structure of Generalized Inverse At,s(1,2)
Fast computing of the Moore-Penrose inverse matrix.
Fast iterative methods for solving Toeplitz-plus-Hankel least squares problems.
Fast Toeplitz Orthogonalization.
Fehleranalyse für die Gauß-Elimination zur Berechnung der Lösung minimaler Länge.
Filter factors of truncated TLS regularization with multiple observations
The total least squares (TLS) and truncated TLS (T-TLS) methods are widely known linear data fitting approaches, often used also in the context of very ill-conditioned, rank-deficient, or ill-posed problems. Regularization properties of T-TLS applied to linear approximation problems were analyzed by Fierro, Golub, Hansen, and O’Leary (1997) through the so-called filter factors allowing to represent the solution in terms of a filtered pseudoinverse of applied to . This paper focuses on the situation...
Hybrid Algorithm for Fast Toeplitz Orthogonalization.
Image restoration through subimages and confidence images.
Least Squares Algorithms for Finding Solutions of Overdetermined Linear Equations Which Minimize Error in an Abstract Norm.
Least squares (P,Q)-orthogonal symmetric solutions of the matrix equation and its optimal approximation.
Least Squares with a Quadratic Constraint.