LSQ Notation: Unusual Notation Explained by Herget 1948

  • Context: Graduate 
  • Thread starter Thread starter solarblast
  • Start date Start date
  • Tags Tags
    Notation
Click For Summary
SUMMARY

The discussion focuses on the LSQ notation introduced by Herget in 1948, specifically addressing the equations (129) and (130). Users express confusion over the notation, particularly the terms (aa) and (ab), which represent weighted summations. The clarification provided indicates that (aa) corresponds to the summation of squares, while (ab) refers to the summation of products. Understanding these notations is crucial for effectively applying the LSQ method in mathematical contexts.

PREREQUISITES
  • Familiarity with LSQ (Least Squares) method
  • Understanding of mathematical notation and summation
  • Basic knowledge of linear algebra concepts
  • Experience with equations and their manipulations
NEXT STEPS
  • Study the derivation and applications of the LSQ method in statistical analysis
  • Learn about the implications of different weighting schemes in summation
  • Explore the historical context and evolution of mathematical notations
  • Review examples of practical applications of Herget's notation in modern mathematics
USEFUL FOR

Mathematicians, statisticians, and students studying linear regression or optimization techniques will benefit from this discussion, particularly those interested in historical mathematical notation and its applications.

solarblast
Messages
146
Reaction score
2
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
    LSQ-Pg47.jpg
    39.5 KB · Views: 496
  • LSQ-Pg48.jpg
    LSQ-Pg48.jpg
    33 KB · Views: 498
Mathematics news on Phys.org
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.
 

Similar threads

Graduate Computation of Solar Position and Velocity Vectors (Meteor Orbit)
  • · Replies 1 ·
Replies
1
Views
2K
Studying Skipping Chapters in Stewart’s Calculus? (Pearson's Edexcel IAL Background)
  • · Replies 2 ·
Replies
2
Views
746
Graduate Kubo Formula Deriviation - interaction picture, complete eigenbasis
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad How is the direction of a harmonic wave expressed?
  • · Replies 6 ·
Replies
6
Views
2K
Addition of Angular Momenta, problem with notation
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Did I figure-out z-translation of 2D-coordinates correctly?
  • · Replies 4 ·
Replies
4
Views
3K
Calculation of current in driven series RLC circuit
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Please Explain Elementary Physics Elevator Question
  • · Replies 22 ·
Replies
22
Views
956
Classical Looking for a physics textbook which shows how to develop theory
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Griffith, Electrodynamics, 4th Edition, Example 4.8. (Second part)
  • · Replies 3 ·
Replies
3
Views
568