QW1 y

It follows from Eq. (5.3.7) that the least squares performance index can be expressed as r 1 1 r 1 ~ 1 2

J(xh n x - (5.4.47) 0 e which for a minimum requires

D1U X = I?1 b. (5.4.48) Since D1/2 is common to both sides of Eq. (5.4.48), the solution is

and X is obtained by backward recursion. Because the diagonals of U are unitary, division by the n diagonal elements is eliminated.

Consider now the use of the square root free Givens transformation to obtain the orthogonal decomposition (Gentleman, 1973). The product W1/2H can be

expressed in component form as

o"ihii 0"ihi2 02^21 0-2^22

where

Now consider the application of the Givens rotation, where any two rows of Eq. (5.4.19) are expressed in the form

0 0

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