Haelterman et al . also showed that when the Quasi-Newton Least Squares Method is applied to a linear system of size, it converges in at most steps although like all quasi-Newton methods, it may not converge for nonlinear systems.
32.
Haelterman et al . also showed that when the Quasi-Newton Inverse Least Squares Method is applied to a linear system of size, it converges in at most steps although like all quasi-Newton methods, it may not converge for nonlinear systems.
33.
This still leaves the question of how to obtain estimators in a given situation and carry the computation, several methods have been proposed : the method of moments, the maximum likelihood method, the least squares method and the more recent method of estimating equations.
34.
When the problem has substantial uncertainties in the independent variable ( the " x " variable ), then simple regression and least squares methods have problems; in such cases, the methodology required for fitting errors-in-variables models may be considered instead of that for least squares.
35.
A spreadsheet application of this for parabolic curves has been developed by NTS . The spreadsheet fits a parabola to 4 or more points ( up to 10 allowed ) using the least squares method and then calculates the limb length ( s ) using Simpson's Rule to evaluate the definite integral.
36.
In 1945 to 1965, Wold proposed and elaborated on his " recursive causal chain " model, which was more appropriate for many applications, according to Wold : For such " recursive causal chain " models, the least squares method was computationally efficient and enjoyed superior theoretical properties, which it lacked for general time-series models.
37.
:See System of linear equations for how to represent a collection of linear equations in the matrix vector form A "'x "'= "'b "'that is used in the description of the linear least squares method .-- Talk 09 : 29, 22 November 2006 ( UTC)
38.
In the next figure the break point is found at X = 7.9 while for the same data ( see blue figure above for mustard yield ), the least squares method yields a break point only at X = 4.9 . The latter value is lower, but the fit of the data beyond the break point is better.
39.
The minimization of "'P1 "'is solved through the conjugate gradient least squares method . "'P2 "'refers to the second step of the iterative reconstruction process wherein it utilizes the edge-preserving total variation regularization term to remove noise and artifacts, and thus improve the quality of the reconstructed image / signal.
40.
The least squares method applied separately to each segment, by which the two regression lines are made to fit the data set as closely as possible while minimizing the " sum of squares of the differences " ( SSD ) between observed ( "'y "') and calculated ( Yr ) values of the dependent variable, results in the following two equations:
