The Adjustment of Observations By the Method of Least Squares With Applications

Cover 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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