weightedNormalEquations

Assemble weighted normal equations.

Developer documentation: this item describes internal implementation details.

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Declaration

 [normalMatrix,rhs] = weightedNormalEquations(X,x,W)

Parameters

• X design matrix
• x observed values
• W weight matrix, vector, scalar, or decomposition

Returns

• normalMatrix weighted normal-equation matrix
• rhs weighted normal-equation right-hand side

Discussion

For the weighted least-squares problem

\[\min_{\xi}\ (x - X\xi)^T W (x - X\xi),\]

this helper returns the normal matrix and right-hand side

\[N = X^T W X, \qquad r = X^T W x.\]

W may be a dense matrix, a diagonal weight vector, a scalar, or a MATLAB decomposition object representing a correlated observation covariance solve.