论文信息 - On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems - 字舞流文

On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems

This paper surveys perturbation theory for the pseudo–inverse (Moore–Penrose generalized inverse), for the orthogonal projection onto the column space of a matrix, and for the linear least squares ...

[1] R. Penrose. A Generalized inverse for matrices , 1955 .

[2] S. Afriat. Orthogonal and oblique projectors and the characteristics of pairs of vector spaces , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[3] L. Mirsky. SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS , 1960 .

[4] Alston S. Householder,et al. The Theory of Matrices in Numerical Analysis , 1964 .

[5] J. H. Wilkinson. The algebraic eigenvalue problem , 1966 .

[6] J. H. Wilkinson,et al. Note on the iterative refinement of least squares solution , 1966 .

[7] Adi Ben-Israel,et al. On Error Bounds for Generalized Inverses , 1966 .

[8] Differentiable generalized inverses , 1968 .

[9] G. Stewart. On the Continuity of the Generalized Inverse , 1969 .

[10] C. Lawson,et al. Extensions and applications of the Householder algorithm for solving linear least squares problems , 1969 .

[11] W. Kahan,et al. The Rotation of Eigenvectors by a Perturbation. III , 1970 .

[12] S. R. Searle. Generalized Inverse Matrices , 1971 .

[13] P. Wedin. Perturbation theory for pseudo-inverses , 1973 .

[14] Adi Ben-Israel,et al. Generalized inverses: theory and applications , 1974 .

[15] A. Sluis,et al. Stability of the solutions of linear least squares problems , 1974 .