# Least Square Minimisation and Partial Differentiation

• skaboy607
In summary, the equation attempts to find a solution to the equation y=-x*F(x,y), where F is a function and x and y are variables. The equation uses partial derivatives with respect to x and y, but when set equal to 0, the "a" in the equation disappears.
skaboy607

## Homework Statement

I am trying to understand how some equations are obtained in some lecture notes I have.

This is my starting equation-http://i423.photobucket.com/albums/pp315/skaboy607/StartEquation.png

And I need to satisfy these conditions

http://i423.photobucket.com/albums/pp315/skaboy607/Conditions.png

And somehow get to here

http://i423.photobucket.com/albums/pp315/skaboy607/WhatIshouldendupwith.png

all above

## The Attempt at a Solution

I've stared at it for a while now and just don't get it. Wouldn't the square come down in front of the brackets? and surely the other constants would dissapear?

any help most appreciated..

Thanks

Last edited by a moderator:
Looking at only one term of the summation, if F=[R1*a - R2*b + R3 - c]^2 (here a, b, and c are constants), then partial of F with respect to R1 is, by the chain rule,

2[R1*a - R2*b + R3 - c]^1 * a,

where a is the derivative of R1*a - R2*b + R3 - c with respect to R1.

But your 2 "disappears" when you set this equal to 0 and divide by 2.

"a" would disappear too, if there were no summation, but in this case "a" is really a_i, so it can't be brought outside of the summation over i.

Nice one, thanks very much.

Hi, I've done this now. But I have just a quick question about it? The way I did it was to multiply the brackets then do partial differentiation with respect to R1, then divide 2 and take out cos(theta) as a common factor. This was quite time consuming, is there something i don't know about that will enable me to look at an equation like that, and jump to final stage like you did so I can miss out the bits in the middle?

Thanks

## 1. What is Least Square Minimisation?

Least Square Minimisation is a mathematical method used to find the line of best fit for a set of data points. It involves minimizing the sum of the squared differences between the actual data points and the predicted values on the line.

## 2. What is the purpose of Least Square Minimisation?

The purpose of Least Square Minimisation is to find the best possible line that represents the relationship between two variables in a data set. This line can then be used to make predictions and analyze the data.

## 3. What is Partial Differentiation?

Partial Differentiation is a mathematical technique used to find the rate of change of a function with respect to one of its variables while holding all other variables constant. It is commonly used in multivariable calculus and optimization problems.

## 4. How is Partial Differentiation related to Least Square Minimisation?

Partial Differentiation is often used in the process of finding the line of best fit in Least Square Minimisation. By taking partial derivatives of the error function with respect to the parameters of the line, we can find the values that minimize the sum of squared errors and determine the equation for the line of best fit.

## 5. What are some applications of Least Square Minimisation and Partial Differentiation?

Least Square Minimisation and Partial Differentiation have a wide range of applications in various fields such as statistics, physics, economics, and engineering. They are commonly used in data analysis, curve fitting, optimization problems, and machine learning algorithms.

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