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Matrix computations (3rd ed.)
Singular value decomposition and least squares solutions
The decomposition of A is called the singular value decomposition (SVD) and the diagonal elements of ∑ are the non-negative square roots of the eigenvalues of A T A; they are called singular values.
Generalized cross-validation as a method for choosing a good ridge parameter
The method of generalized cross-validation (GCV) for choosing a good value for λ from the data is studied, which can be used in subset selection and singular value truncation methods for regression, and even to choose from among mixtures of these methods.
Numerical solution of saddle point problems
A large selection of solution methods for linear systems in saddle point form are presented, with an emphasis on iterative methods for large and sparse problems.
Calculating the singular values and pseudo-inverse of a matrix
The use of the pseudo-inverse $A^I = V\Sigma ^I U^* $ to solve least squares problems in a way which dampens spurious oscillation and cancellation is mentioned.
The differentiation of pseudo-inverses and non-linear least squares problems whose variables separate
  • G. Golub, V. Pereyra
  • Computer Science, Mathematics
    Milestones in Matrix Computation
  • 1 February 1972
Algorithms are presented which make extensive use of well-known reliable linear least squares techniques, and numerical results and comparisons are given.
Missing value estimation for DNA microarray gene expression data: local least squares imputation
Imputation methods based on the least squares formulation are proposed to estimate missing values in the gene expression data, which exploit local similarity structures in the data as well as least squares optimization process.
An analysis of the total least squares problem
  • G. Golub, C. Loan
  • Mathematics
    Milestones in Matrix Computation
  • 1 February 1980
An algorithm for solving the TLS problem is proposed that utilizes the singular value decomposition and which provides a measure of the underlying problem''s sensitivity.
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
A new method for solving total variation (TV) minimization problems in image restoration by introducing an additional variable for the flux quantity appearing in the gradient of the objective function, which can be interpreted as the normal vector to the level sets of the image u.