# Normal equation

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Related to Linear least squares: Nonlinear least squares

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Also found in: Encyclopedia, Wikipedia.

Related to Linear least squares: Nonlinear least squares

By fixing two factor matrices alternately at each iteration, three coupled linear least squares subproblems are then formulated to find each factor matrix:

Thus, the original nonlinear optimization problem can be solved with a sequence of three linear least squares problems.

Using non-full-rank design matrices and numerous models, Monahan covers the linear least squares problem, estimability and least squares estimators, the Gauss-Markov model, distributional theory, statistical inference, topics in testing (such as orthogonal polynomials and contrasts), variance components and mixed models, and the multivariate linear model.

3) fill length data was replotted against %DF/(100-%DF) and a straight line was fitted to the data for each screw, using the linear least squares regression method.

sc] can be obtained by a linear least square fit of the experimental data to Eq 10.

The firm proudly called it a "stepwise population-weighted linear least squares method" to work out policing.

Average annual rates mentioned in the text and tables are based on the linear least squares trend of the logarithms of the index numbers.

It is clear that for a fixed value of a the linear parameters c can be found by solving a linear least squares problem.

Covered in the 2004 edition are the calculation of linear least squares, the numerical analysis of functional integral and integro-differential equations of Volterra type, sparse grids, complete search in continuous global optimization and constraint satisfaction, and multiscale computational modeling of the heart.

When applying the linear least squares analysis to Eq 8, it is assumed that the error is constant or randomly distributed.

HEATH, AND ESMOND NG, A Comparison of Some Methods for Solving Sparse Linear Least Squares Problems, SIAM J.

In over 100 exercises, supported by the accompanying CD-ROM, she describes probability concepts, discrete probability distributions, continuous probability distributions, mathematical expectation, limit theorems, transitions to statistics, estimating theory, hypothesis testing theory, order statistics and quantiles, permutation analysis, bootstrap analysis, multiple sample analysis, linear least squares analysis and contingency truth analysis.

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