0
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1answer
85 views

First derivative of Lagrange polynomial

Given the Lagrange basis polynomial as: $L_i(x)= \prod_{m=0, m \neq i}^n \frac{x-x_m}{x_i-x_m} $ is there a generic equation for the first derivative ${L_i}'(x)$ for any order,t hat is for any $n$?
1
vote
2answers
49 views

total least squares derivation with matrices

Taken from a computer vision book: "to minimize the sum of the perpendicular distances between points and lines, we need to minimize $$ \sum_i (ax_i + by_i +c)^2$$ subject to $a^2 +b^2 =1$. Now using ...
2
votes
3answers
104 views

Lagrange multipliers from hell

I was asked to solve this question, decided to try and solve it with lagrange multipliers as I see no other way: "Find the closest and furthest points on the circle made from the intersection of the ...
2
votes
3answers
96 views

Lagrange Method Problem

I am from engineering background and I am currently studying calculus. I had a question from assignment to be solved from a course on coursera but I could not do it. People have posted solution in the ...
1
vote
1answer
41 views

How do I setup the lagrangian for this problem?

I have a function $y(x)$, that I would like to maximize, subject to two constraints. It is given by: $$ \max_{x} \ y(x) = a \ cos(x) + b \ sin(x) \\ \text{subject to:} \\ x \geq 0 \\ x \leq ...
1
vote
0answers
29 views

How can I find the Min and max of this question?

I have been trying for the past 2 hours on this question and cannot seem to figure out the answer. So far I have gotten the 'green' bits correct. Someone Help please
1
vote
2answers
44 views

How can I solve this using the Lagrange method?

This is what I keep doing but the answer seems to be wrong every time.
2
votes
1answer
289 views

How to restrict Lagrange multiplier on positive values?

Here's the function that i want to optimize: $$f(x,y) = x-2y$$ and the constraint is: $$g(x,y) = x^2 + y - 10 = 0$$ Solving with Lagrange multiplier I get: $$F(x,y) = x-2y - x^2\lambda - y\lambda ...
1
vote
1answer
76 views

What is the constraint in this LaGrange Multipliers ??

$x$ and $y$ are real numbers where satisfied the equation $x^2+y^2+xy-3x-3y-9=0$ Find the max. and min. values of $x^2+y^2$ I don't know how to find the constraint
1
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1answer
157 views

Lagrange method - non-linear system of equations

I have to compute optimal parametres of truncated cone so that its Volume is fixed (lets say it is 1) and its surface is minimal using Lagrange method These are equations desribing my object: ...