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.

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.

References in periodicals archive ?
10) to the normal equations associated with the matrix linear operator defined by (4.
The classical LSQR algorithm is analytically equivalent to the conjugate gradient method applied to the associated normal equation.
The reduced minimization problem is solved by the direct least squares method, by the global LSQR, by the preconditioned conjugate gradient method for the normal equation (GPCG), and by the Hu-Reichel method (HR).
The translation parameters are canceled out from the Normal equations and, therefore, can be removed from the Equations (2) and (4).
To derive the Normal equations for the multivariate model, we take partial derivatives of Q([b.
Usually solving the normal equations is preferred to solving the KKT system, because the matrix for the normal equations is much smaller.
16) is satisfied, we form and solve the normal equations on the CPU.
We compared these two options with our full double precision MATLAB implementation (6) without using the GPU for solving the normal equations (3.
This causes overhead in factorization of dense normal equations matrices.
The iteration count in parentheses represents the number of iterations at which the GPU is used for assembling and factoring the matrix for the normal equations.
At each iteration, we transfer only a few vectors, including the right-hand side of the normal equation (3.