Extensions to the modified Gram-Schmidt strategy and its application in the steepest ascent method
The orthogonalization of undesigned experiments is introduced to increase statistical precision of the estimated regression coefficients. The goals are to minimize the covariance and the bias of the least squares estimator for estimating the path of the steepest ascent (SA) that leads the users toward the neighbour of the optimum response. An orthogonal design is established to decrease the inverse determinant of X'X and the angle between the true and the estimated SA paths. For orthogonalization of an undesigned matrix, our proposed solution is constructed on the modified Gram-Schmidt strategy relevant to the process of Gaussian elimination. The proposed solution offers an orthogonal basis, in full working accuracy, for the space spanned by the columns of the original matrix.
orthogonalization least square steepest ascent path