LSQ Notation: Unusual Notation Explained by Herget 1948

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Discussion Overview

The discussion centers around the unusual notation used in the LSQ (Least Squares) method as described by Herget in 1948, specifically focusing on the equations labeled (129) and (130). Participants are trying to clarify the meaning and implications of this notation.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant expresses confusion regarding the notation (aa) and its meaning in the context of the LSQ method as presented in the attached pages.
  • Another participant suggests that the notation becomes clearer in equation (130), providing examples of how (aa) and (ab) relate to summations involving variables x and y.
  • A third participant proposes that by setting all weights to one in equation (130), one can derive equation (129) with explicit summations, indicating a method to understand the notation better.
  • A later reply confirms the previous participant's suggestion as being reasonable.

Areas of Agreement / Disagreement

Participants generally agree that the notation is unclear, but there is no consensus on its interpretation. Multiple viewpoints on how to approach understanding the notation remain present.

Contextual Notes

The discussion highlights the potential limitations in understanding the notation due to its unfamiliarity and the specific historical context of Herget's work. There may be unresolved assumptions regarding the definitions of the terms used in the equations.

Who May Find This Useful

Readers interested in the historical development of mathematical notation, the LSQ method, or those studying Herget's work may find this discussion relevant.

solarblast
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See the two pages I've attached. 47 and 48. I'm trying to understand the notation used for the (129) equations. A hint is just below the equations. ( ) ∑. These pages are describing the LSQ method. (aa), etc. aa doesn't make sense to me. Herget devised this notation in 1948.

Comments
 

Attachments

  • LSQ-Pg47.jpg
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  • LSQ-Pg48.jpg
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solarblast said:
See the two pages I've attached. 47 and 48. I'm trying to understand the notation used for the (129) equations. A hint is just below the equations. ( ) ∑. These pages are describing the LSQ method. (aa), etc. aa doesn't make sense to me. Herget devised this notation in 1948.

Comments
It's not very clear, but the stuff in (130) gives a better idea. For example, the notations (aa) x and (ab) y mean, respectively,
$$ x \sum_{i = 1}^n (a_i)^2$$
and
$$ y \sum_{i = 1}^n a_i b_i$$
 
The notation is unfamiliar to me but it's written in a more common form in Eq. 130. Just set all the weights to one in Eq. 130 to find Eq. 129 with explicit summations.
 
Sounds about right.
 

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