LSQ Notation: Unusual Notation Explained by Herget 1948

[solarblast]

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

 

[Mark44]

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
$$ y \sum_{i = 1}^n a_i b_i$$

 

[rikblok]

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.

 

[solarblast]

Sounds about right.

 

[CellCoree]

:

Thank you for sharing your question about the LSQ notation and its explanation by Herget in 1948. I can understand your confusion about the notation used in the (129) equations. The notation (aa), etc. may not make sense at first glance, but it is actually a shorthand way of representing a summation of terms.

The symbol ( ) ∑ is typically used to indicate a summation, where the variable inside the parentheses is the index of summation. In this case, (aa) indicates that the terms being summed are represented by the variable "aa." The notation (aa), etc. simply means that the summation includes additional terms that follow the same pattern.

Herget's use of this notation may have been influenced by his background in mathematics, where this shorthand notation is commonly used. It may seem unusual to someone unfamiliar with it, but it is a valid and efficient way of representing summations.

I hope this helps to clarify the notation used in the (129) equations and provides a better understanding of Herget's explanation. If you have any further questions about the LSQ method or its notation, please do not hesitate to ask. Thank you for your interest in this topic.