The Adjustment of Observations By the Method of Least Squares With Applications
The Adjustment of Observations By the Method of Least Squares With Applications
T W Thomas Wallace Wright
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. = /i weight i, bny + 6-0^ + . . . = 4 " 1, [^]j' + U->+. ■ •=[/] " -)• [For the normal equations found from the first set after eliminating x are the same as the normal equations formed from the second set directly, ] Ex. 6. — Instead of the observation equation ax + by + cz + . . . = / weight /, we may write gax + qby + . . . = ql weight —^_- 78. Control of the Formation of the Normal Equations. — A very convenient check or control is the following. Add as an extra term to each observation e...quation the sum of the coeffi- cients of X, V, . . . And of the absolute term / in that equation, and treat these added terms just as we do the absolute terms. Thus let s^, J-. , . . . S, ^^ denote the sums, so that a^ + l\ + Ci + ■ ■ •+/!== si, a. , + b.. + r, + • • • + /. , =, v, , (Tn + ^>n + (', 1 + ■ ■ • + hi = -^n Multiply each of these expressions by its a and add the prod- ucts, each by its d and add, and so on ; then [aa] + [ab^ -!-••• + [al] = [as], [ob] + [bb] + ■ .
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