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Least squares
International Tables for Crystallography (2006). Vol. C, ch. 8.1, pp. 678-688 [ doi:10.1107/97809553602060000609 ]
... of the transposes of the factors in reverse order: (AB)T= BTAT. The trace of a square matrix is the sum ... all eigenvalues are real, and there exists a unitary matrix, T, such that is diagonal, with the elements of D equal to the eigenvalues of A, and the columns of T are the eigenvectors. An n × n symmetric matrix therefore ...
Orthogonal distance regression
International Tables for Crystallography (2006). Vol. C, Section 8.1.6, pp. 687-688 [ doi:10.1107/97809553602060000609 ]
... that exploit this structure exist; one has been given by Boggs, Byrd & Schnabel (1987), and the software, called ODRPACK, is by Boggs, Byrd, Donaldson & Schnabel (1989). The algorithm is based on ... procedure for the computation of the variance-covariance matrix, see Boggs & Rogers (1990). References Boggs, P. T., Byrd, R. ...
Conjugate-gradient methods
International Tables for Crystallography (2006). Vol. C, Section 8.1.5.2, pp. 686-687 [ doi:10.1107/97809553602060000609 ]
... is (1) define ; (2) for k = 0, 1, 2, ..., p - 1, (a) ; (b) ; (c) ; (d) . This algorithm finds the ... exact solution for the quadratic function in not more than p steps. This algorithm cannot be used directly for the nonlinear ... an actual line search, and the termination after at most p steps is replaced by a convergence test. Thus, we ...
[more results from section 8.1.5 in volume C]
Recommendations
International Tables for Crystallography (2006). Vol. C, Section 8.1.4.5, p. 685 [ doi:10.1107/97809553602060000609 ]
... International Tables for Crystallography (2006). Vol. C, ch. 8.1, p. 685 © International Union of Crystallography 2006 | home | resources | advanced search ...
[more results from section 8.1.4 in volume C]
Conditioning
International Tables for Crystallography (2006). Vol. C, Section 8.1.3.3, p. 682 [ doi:10.1107/97809553602060000609 ]
... design matrix, Z, into the form where S is a p × p diagonal matrix whose elements define some kind of `natural' unit ... International Tables for Crystallography (2006). Vol. C, ch. 8.1, p. 682 © International Union of Crystallography 2006 | home | resources | advanced ...
[more results from section 8.1.3 in volume C]
Principles of least squares
International Tables for Crystallography (2006). Vol. C, Section 8.1.2, pp. 680-681 [ doi:10.1107/97809553602060000609 ]
... have a unique minimum at . The matrix is a p × n matrix that relates the n-dimensional observation space to the p-dimensional parameter space and is known as the least-squares ... principle. Hayward, CA: Institute of Mathematical Statistics. Box, G. E. P. & Tiao, G. C. (1973). Bayesian inference in statistical ...
Statistics
International Tables for Crystallography (2006). Vol. C, Section 8.1.1.2, pp. 679-680 [ doi:10.1107/97809553602060000609 ]
Statistics 8.1.1.2. Statistics A probability density function, which will be abbreviated p.d.f., is a function, [Phi](x), such that the probability of finding the random variable x in the interval is given by A p.d.f. has the properties and A cumulative distribution function, which will be abbreviated c.d.f., is defined by ...
[more results from section 8.1.1 in volume C]
Software for least-squares calculations
International Tables for Crystallography (2006). Vol. C, Section 8.1.7, p. 688 [ doi:10.1107/97809553602060000609 ]
... International Tables for Crystallography (2006). Vol. C, ch. 8.1, p. 688 © International Union of Crystallography 2006 | home | resources | advanced search ...
International Tables for Crystallography (2006). Vol. C, ch. 8.1, pp. 678-688 [ doi:10.1107/97809553602060000609 ]
... of the transposes of the factors in reverse order: (AB)T= BTAT. The trace of a square matrix is the sum ... all eigenvalues are real, and there exists a unitary matrix, T, such that is diagonal, with the elements of D equal to the eigenvalues of A, and the columns of T are the eigenvectors. An n × n symmetric matrix therefore ...
Orthogonal distance regression
International Tables for Crystallography (2006). Vol. C, Section 8.1.6, pp. 687-688 [ doi:10.1107/97809553602060000609 ]
... that exploit this structure exist; one has been given by Boggs, Byrd & Schnabel (1987), and the software, called ODRPACK, is by Boggs, Byrd, Donaldson & Schnabel (1989). The algorithm is based on ... procedure for the computation of the variance-covariance matrix, see Boggs & Rogers (1990). References Boggs, P. T., Byrd, R. ...
Conjugate-gradient methods
International Tables for Crystallography (2006). Vol. C, Section 8.1.5.2, pp. 686-687 [ doi:10.1107/97809553602060000609 ]
... is (1) define ; (2) for k = 0, 1, 2, ..., p - 1, (a) ; (b) ; (c) ; (d) . This algorithm finds the ... exact solution for the quadratic function in not more than p steps. This algorithm cannot be used directly for the nonlinear ... an actual line search, and the termination after at most p steps is replaced by a convergence test. Thus, we ...
[more results from section 8.1.5 in volume C]
Recommendations
International Tables for Crystallography (2006). Vol. C, Section 8.1.4.5, p. 685 [ doi:10.1107/97809553602060000609 ]
... International Tables for Crystallography (2006). Vol. C, ch. 8.1, p. 685 © International Union of Crystallography 2006 | home | resources | advanced search ...
[more results from section 8.1.4 in volume C]
Conditioning
International Tables for Crystallography (2006). Vol. C, Section 8.1.3.3, p. 682 [ doi:10.1107/97809553602060000609 ]
... design matrix, Z, into the form where S is a p × p diagonal matrix whose elements define some kind of `natural' unit ... International Tables for Crystallography (2006). Vol. C, ch. 8.1, p. 682 © International Union of Crystallography 2006 | home | resources | advanced ...
[more results from section 8.1.3 in volume C]
Principles of least squares
International Tables for Crystallography (2006). Vol. C, Section 8.1.2, pp. 680-681 [ doi:10.1107/97809553602060000609 ]
... have a unique minimum at . The matrix is a p × n matrix that relates the n-dimensional observation space to the p-dimensional parameter space and is known as the least-squares ... principle. Hayward, CA: Institute of Mathematical Statistics. Box, G. E. P. & Tiao, G. C. (1973). Bayesian inference in statistical ...
Statistics
International Tables for Crystallography (2006). Vol. C, Section 8.1.1.2, pp. 679-680 [ doi:10.1107/97809553602060000609 ]
Statistics 8.1.1.2. Statistics A probability density function, which will be abbreviated p.d.f., is a function, [Phi](x), such that the probability of finding the random variable x in the interval is given by A p.d.f. has the properties and A cumulative distribution function, which will be abbreviated c.d.f., is defined by ...
[more results from section 8.1.1 in volume C]
Software for least-squares calculations
International Tables for Crystallography (2006). Vol. C, Section 8.1.7, p. 688 [ doi:10.1107/97809553602060000609 ]
... International Tables for Crystallography (2006). Vol. C, ch. 8.1, p. 688 © International Union of Crystallography 2006 | home | resources | advanced search ...
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