Normal Equations

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normal equations

[¦nȯr·məl i′kwā·zhənz]
The set of equations arising in the least squares method whose solutions give the constants that determine the shape of the estimated function.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Normal Equations


a set of algebraic or transcendental equations whose solution gives the approximate values of unknown quantities that can be derived by the method of least squares.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
In Section 2, we present the RSSI channel model and the weighted linear least squares location estimator.
Given the flat prior for the Tx position [m.sub.j] and the improper prior p(l/[b.sub.j]) [infinity] [[absolute value of [1/[b.sub.j]].sub.-1], the posterior of ([m.sub.j], 1 /[b.sub.j]) is thus given by the standard linear least squares (LLS) formulas
Once the calibration measurements have been completed, a Python script performs the linear least squares fit and covariance matrix computations to generate a report including the Steinhart-Hart coefficients and uncertainty in a temperature measurement at each of the calibration points.
Inertia Estimation Using Linear Least Squares. The rotational dynamics of a rigid body is described as [14]
Furthermore, given a good initial point and the Taylor series expansion technology [6, 7], the highly nonlinear joint estimation problem of location and biases can be reduced to a linear least squares issue, which called TS-LQP.
Note that once A is solved, then C can be handled by linear least squares methods.
Linear Least Squares Method in T M D the Time Domain (Prony classical version [8]; ARMA / ARX/IIR+OE versions [5][9][6]) Least Squares Complex Exponential T M I Method (LSCE) [5][10][7] Ibrahim Time Domain Method T M I ([5] [11]; Single Station Time Domain Method (SISO version) [12][13][14]) Stochastic Subspace T M D identification Methods [15][16][17][18] Linear Least Squares Method in F M D the Frequency Domain (Classical Zobel-Levy [8]; Prony method [5][19]; Rational Fraction Polynomial [5][20]) Basic Methods in the Frequency F S I Domain (Peak Picking Amplitude, Quadrature Response/Max.
Linear least squares estimation of yield based on cutting bill requirements is a viable concept provided the cutting bills used adhere to the framework (i.e., part sizes and part quantities) established for the model.
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.
The firm proudly called it a "stepwise population-weighted linear least squares method" to work out policing.