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- Publications
- Influence
Singular value decomposition and least squares solutions
- G. Golub, C. Reinsch
- Mathematics, Computer Science
- Milestones in Matrix Computation
- 1 April 1970
Let A be a real m×n matrix with m≧n. It is well known (cf. [4]) that
$$A = U\sum {V^T}$$
(1)
where
$${U^T}U = {V^T}V = V{V^T} = {I_n}{\text{ and }}\sum {\text{ = diag(}}{\sigma… Expand
Generalized cross-validation as a method for choosing a good ridge parameter
Consider the ridge estimate (λ) for β in the model unknown, (λ) = (X T X + nλI)−1 X T y. We study the method of generalized cross-validation (GCV) for choosing a good value for λ from the data. The… Expand
Numerical solution of saddle point problems
Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties,… Expand
Calculating the singular values and pseudo-inverse of a matrix
A numerically stable and fairly fast scheme is described to compute the unitary matrices U and V which transform a given matrix A into a diagonal form $\Sigma = U^ * AV$, thus exhibiting A’s singular… Expand
The differentiation of pseudo-inverses and non-linear least squares problems whose variables separate
- G. Golub, V. Pereyra
- Mathematics, Computer Science
- Milestones in Matrix Computation
- 1 February 1972
For given data ($t_i\ , y_i), i=1, \ldots ,m$ , we consider the least squares fit of nonlinear models of the form F($\underset ~\to a\ , \underset ~\to \alpha\ ; t) = \sum_{j=1}^{n}\ g_j (\underset… Expand
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
We study efficient iterative methods for the large sparse non-Hermitian positive definite system of linear equations based on the Hermitian and skew-Hermitian splitting of the coefficient matrix.… Expand
Missing value estimation for DNA microarray gene expression data: local least squares imputation
- H. Kim, G. Golub, Haesun Park
- Medicine, Computer Science
- Bioinform.
- 15 January 2005
MOTIVATION
Gene expression data often contain missing expression values. Effective missing value estimation methods are needed since many algorithms for gene expression data analysis require a… Expand
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
We present a new method for solving total variation (TV) minimization problems in image restoration. The main idea is to remove some of the singularity caused by the nondifferentiability of the… Expand