1
vote
0answers
29 views

Fourier Interpolation

I have this Equation, that I modeled from my measurements and simulations. $I^{exp}_{l,m} = (\mathbf{F}^{H}.\mathbf{A}.I^{true})_{l,m}$; $H$ is the Hermitian transpose and $\mathbf{F}^{H}$ is a block ...
0
votes
1answer
45 views

Reverse range of numbers, scaling

I have a float that goes from 1 to 0 .Im trying to make it so that the order is reversed and scaled so it goes from 0 to -80 Just wondering if there is a straight forward way to do this?
2
votes
0answers
31 views

Smallest set of Liner equations, which exactly fit a set of points

I have a set of 2-d points,(it can be of any arbitrary dimension n). I want to find the minimum set of straight lines(linear equations) which exactly passes through the given 2-d points (unlike ...
0
votes
1answer
71 views

smooth orientation change with quaternions

My camera orientation is looking in the $v_1$ direction. Something happens on direction $v_2$ and I want the camera to move smoothly to look at that direction. So, to find the quaternion to go from ...
1
vote
2answers
81 views

Polynomial Interpolation

My professor gave the following question as a practice for study guide. Any assistance in terms of helping me to solve this would be much appreciated. Suppose that $f$ is continuous and has ...
1
vote
1answer
132 views

how covert joysitck (x, y) coordinates to robot motor speed?

I am trying to formulate an equation to calculate left and right motor speeds of a robot. The robot is four wheeled drive with independent motors connected to tank-like best on each side. see this ...
0
votes
1answer
45 views

Rotation matrix for non-isometry transformation

Imagine that you have a sphere in $\mathbb{R}^3$ and a plane (that is parallel to the x,y plane) through the sphere. Now you want to have a clockwise rotation in the x/y plane that does the ...
0
votes
1answer
230 views

Calculating Log-likelihood using Raphson and Jacobian matrices?

I am reading the following paper: http://www.ntuzov.com/Nik_Site/Niks_files/Research/papers/stat_arb/Ahmed_2009.pdf and in particular page 13. I want to try and calculate lambda_t(p) = exp^(Beta^T ...
2
votes
1answer
184 views

How do I apply the Fast Multipole Method to Thin Plate Spline interpolation?

I have n scattered measurements of elevation, z, as a function of x and y coordinate: $ \{(x_i,y_i,z_i)\}_{i=1..n}$ that I want to interpolate so that I find z(x,y) for all x and y. Using Thin Plate ...
0
votes
0answers
46 views

interpolation and Vandermonde

Looking at a problem of interpolation, I find a Vandermonde type matrix. To be precise I consider the following, let $$A(z)= \sum_{i=1}^p \sum_{j=2}^{n_i+1}\frac{a_{i}^j}{(z-z_i)^j}$$ where the $z_i$ ...
1
vote
1answer
441 views

Thin Plate Spline interpolation of scattered $z(x,y)$ data

I am trying to understand Thin Plate Spline interpolation of scattered data. As I understand it TPS is just a special case of Radial Basis Function interpolation: $$ z(x,y) = p(x,y) + \sum_i ...
2
votes
1answer
55 views

Is there a nice way to interpret this matrix equation that comes up in the context of least squares

So I am working on this problem with fitting a second degree polynomial of the form $y=a_1x^2+a_2x+a_3$ to four points using least squares. One of the parts of the problem is to write out the matrix ...
1
vote
1answer
56 views

What are the explicit expression for this interpolation problem

We want to fit $f(x) = a_0 + a_1 *x + a_2 * x^2 + ... + a_n * x^n$ to the data $(x_i,f(x_i))$ for $i = 0 ... n.$ It will give rise to the following system $ A a = b $ Here $ a = [ a_1 a_2 a_3 ...
1
vote
2answers
65 views

What is the equation stands for in geometry(intuitively)?

I am writing a bilinear interpolation method. This method can be abstract by solve the equation A*x = b, A is a 4x4 matrix below: $A=\begin{pmatrix} 1 &x_1 &y_1 &x_1y_1\\ 1 ...
0
votes
1answer
3k views

How to perform simple linear interpolation on a data set

With the following data set, what is the best way to interpolate the data for each time. ...
2
votes
2answers
944 views

given $y = a + bx + cx^2$ fits three given points, find and solve the matrix equation for the unknowns $a,b$, and $c$

Given $y = a + bx + cx^2$ fits three given points, find and solve the matrix equation for the unknowns $a$, $b$, and $c$. the equation fits the points $(1,0), (-1, -4),$ and $(2, 11)$ I really ...
1
vote
3answers
1k views

Linear Algebra Question (Polynomial Interpolation)

Given the data for an experiment: Velocity: 0, 2, 4, 6, 8, 10 Force: 0 , 2.9, 14.8, 39.6, 74.3, 119 (One force value listed below one velocity value in a table) Find an interpolating ...
0
votes
1answer
140 views

Vandermonde and curve interpolation

I hesitate here because of an understanding with a calculation problems. I want to calculate an interpolation using the Vandermonde matrix. see: http://en.wikipedia.org/wiki/Vandermonde_matrix My ...
3
votes
1answer
279 views

How to minimize this function difference

Sorry about this somewhat lengthy introduction to my question. I thought it might be useful to know what I'm trying to do. I decided that I would like to have sequence of polynomials in $\mathbb{P}_n ...
5
votes
1answer
358 views

Determining Coefficients of a Finite Degree Polynomial $f$ from the Sequence $\{f(k)\}_{k \in \mathbb{N}}$

Suppose $f$ is an unknown polynomial of degree $n$ (in one indeterminate) but the sequence $\{ f(k) \}_{k \in \mathbb{N}}$ is given. It is a nice exercise to show that one needs only the first $n+1$ ...