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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 result of the series analysis yield time series normal equation characteristic of Ekulu river stretch studied.

The normal equation for computing [DELTA]y is a positive definite and symmetric matrix but the normal equation for computing [DELTA]x is not symmetric.

17) are normal equations, so they can be solved by cholesky factorization.

The optimal solution to the LSP at instant k can be found by solving the normal equation.

At each iteration, we transfer only a few vectors, including the right-hand side of the normal equation (3.

The game might still be drawn although with a match run rate of over four per over, normal equations are inapplicable.

A],) are canceled out from the Normal equations by shifting the given data to the origin (i.

Note: The values of (a) and (b) obtained from the Normal equations correspond to a minimum value for the quadratic function Q(a,b) given by equation (4), as can be easily demonstrated by using the optimization methodology of differential calculus for functions of two independent variables.

Hudson of the CSIRO Computing Research Section wrote the sub-routine for solution of the normal equations, based on the method of Cholesky.

With the equation in this form, there are two more coefficients to be estimated than there are independent normal equations.

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