Compact Numerical Methods for Computers
By John C. Nash. 2018
360 citations recorded by the source corpus.
A starting point Formal problems in linear algebra The singular-value decomposition and its use to solve least-squares problems Handling larger problems Some comments on the formation of the cross-product matrix ATA Linear equations-a direct approach The Choleski decomposition The symmetric positive definite matrix again The algebraic eigenvalue generalized problem Real symmetric matrices The generalized symmetric matrix eigenvalue problem Optimization and nonlinear equations One-dimensional problems Direct search methods Descent to a minimum I-variable metric algorithms Descent to a minimum II-conjugate gradients Minimizing a nonlinear sum of squares Leftovers The conjugate gradients method applied to problems in linear algebra Appendices Bibliography Index
Subfields: Computational Theory and Mathematics, Numerical Analysis
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In Computational Theory and Mathematics
In Numerical Analysis
Citations in the corpus
- Asymptotic efficiency of the two-stage estimation method for copula-based models (2005, background): “, [15]) for the two-stage estimation procedure, only the likelihoods (univariate and multivariate) need to be coded; even the inference functions in (2.”
- Copula-Based Models for Multivariate Discrete Response Data (2013, methodology): “Since the estimation of the parameters of the copula-based models is obtained using a quasi-Newton routine [36] applied to the joint log-likelihood in (11.”
- A bound constrained conjugate gradient solution method as applied to crystallographic refinement problems (2005, methodology): “Invariably, the Newton–Raphson method of non-linear least squares is used with the Marquardt (1963) method included for stability. The normal equations are generated by expansion of the calculated pattern to a first-order Taylor series around the parameter vector, ignoring second-order terms. The re”
- Regression in a copula model for bivariate count data (2010, methodology): “Various optimization methods such as the quasi-Newton method [22] and the robust Nelder–Mead algorithm [23] can be used.”