Interpolation Definition and 136 Threads

I don't need any help for the engineering maths I'll be doing after but if I anyone could advise me on how to write a program that would take a set of x and y values and then give me back the y values at certain intervals on the x-axis I would be very grateful. I've got colossal amounts of data...

Homework Statement I have been trying to learn how to use linear interpolation to find out the data needed from the thermodynamics chart, however, the book that is assigned does not even talk about it. Could someone please explain how linear interpolation is used? Thanks

Hi, I'm doing a project in medicine, I've used MATLAB to create 3d graphs using a vector with 5 fixed values as X, a vector with 7 fixed values as Y. As Z I have 5*7 measured values. I need to interpolate my graph to "smoothen" the lines in the graph, but I am totaly lost, I have no idea how...

For a second order differential equation, is it necessary to derive a weak form if quadratic interpolation are used?

Basically I've got to design and develop a software for computing a polynomial function involving a set of data points. I've got to use an algorithm based on the lagrange interpolation method. I know it should involve two loops inside the code. What I've been told is that "The input to the...

Homework Statement If i have an interpolation formula, say: y(t_i)=3+h\sum^i_{j=1}jy(t_j) where i=0 to n h=(a+b)/n ti=i*h and when i=0, we have: y(t0)=0. How would i write a code to find y(ti)? Homework Equations The Attempt at a Solution function y=examp(a,b,n)...

I have a non-uniform grid within which velocity data is known at each grid point. This velocity data is to be interpolated to allow for evaluation of velocity at an arbitrary point inside the grid. I am wondering about the correct approach to this problem. In actuality I want to evaluate the...

Hi everyone. I'm doing a microcontroller project where I'm using a 256 element array of 1 byte values to output a sine wave at varying frequencies. I'm using the top 8 bytes of a 16 bit "angle increment" value that's incremented by varying amounts as an index to the array of values, to control...

Hi everyone, I have a question about interpolation methods. I am given two particles and I know their positions, velocities, accelerations, and jerks (time derivative of acceleration) at some initial and final time-values (t0 and t1, respectively). I want to find the minimum distance...

Homework Statement Consider the use of cubic splines to interpolate a set of data. Suppose at some stage in the calculation we arrive at the following spline functions for two consecutive intervals \tilde{f_{0}} = x^{3} + ax^{2} + bx + c over the interval -1 \leq x \leq 1 \tilde{f_{1}} =...

Hello, I'm having a really hard time doing some work in Matlab, I have a book but it just isn't making sense to me, the problem I have to do is in four parts so Ill just show the first part for now... The following coordinates specify the shape of a certain cars’ front fender. Interpolate...

Interpolation ? A treatment plant consists of a primary sedimentation tank followed by a trickling filter that removes 80% of the influent BOD. The flow is then directed to a constructed marsh system that has an influent target BOD concentration of 30 mg/l before being discharged to a small...

Homework Statement Given points (x0,y0), (x1, y1)...(xn,yn) and derivatives at each of these points y'0, y'1...y'n : Write a program to find the interpolating polynomial (of degree 2n+1) and to evaluate it on given points xeval. My question is what type of interpolation is this? I'm not...

Hi all, http://www.bsodmike.com/stuff/interpolation.pdf" I am going through some of my notes and quite a few books; they all skip the over the point I have marked with 3 red dots in the http://www.bsodmike.com/stuff/interpolation.pdf" . \begin{equation}\label{eq:solution}\begin{split}...

I have to find a system of linear equations to determine a quadratic polynomial p(x) = ax2+bx+c Given the conditions: p(1) = f(1) p'(1) = f'(1) p''(1) = f''(1) where f(x) = xex-1 I know: p(x) = ax2+bx+c p'(x) = 2ax +b p''(x) = 2x f(x) = xex-1 f'(x) = ex-1 +...

Hi, I've been given a problem to solve and I was hoping for some pointers. To start with we have a surface which is originally represented as a Bezier patch, a peicewise set of bi-cubic bezier surfaces. It might be important to mention that the surface is "fairly two dimensional", the surface...

i have solved a differential equation with shooting methods, the output is in form of interpolate function, i can see it with a graphics, but i i would have an approssimate analitic form what kind of function i have to do ? the equation give in output have this form...

http://img337.imageshack.us/img337/8922/problemcmi0.jpg Can anyone explain to me please how this problem is solved ?

Hi, i have no idea how to start up my program on Newton interpolation. i have solved it manually but I am clueless on how 2 start my program. below represnts the input which i want 2 solve. every 4 lines represnts one problem. the 1st line- n,m where n is no of data points and m is no of...

Can anyone tell me what is the equation for First Order of Newton’s Interpolation? The one of Interpolation I know is Lagrange’s Interpolation such as p(x)= \frac {x-x1}{x0-x1} f(x0) + \frac {x-x0}{x1-x0} f(x1) and so on ... Thanks in advance

Attached below are two cubic spline tutorials: 1. Explanation of the classic tri-diagonal cubic spline formulation. Included are 2 example problems. 2. Extension to parametric cubic splines. Included are 2 example problems . :smile:

Homework Statement Given a set of data points, derive the interpolation polynomial using divided differences. Homework Equations The Attempt at a Solution My main question is: How am I supposed to do this if they don't give f(x)? Can I just look at the plotted data points and...

Homework Statement If 0 < \alpha < n, define an operator T_{\alpha} on function on \mathbb{R}^n by T_{\alpha}f(x) = \int |x-y|^{-\alpha}f(y)dy Then prove that T_{\alpha} is weak type (1,(n-\alpha )^{-1}) and strong type (p,r) with respect to Lebesgue measure on \mathbb{R}^n, where 1 < p <...

I completely forgot how to do this. I have a thermo test coming up and i will be interpolating a lot of data. What is the fastes/easiest way to interpolate a point on a chart not given?

The problem is described here: http://phstudy.technion.ac.il/~wn117066/Problems2.pdf In question 1 I need to find the refractive indices for both polarizations at 760nm. I'm not quite sure how to go about this - which model of dispersion best fits Calomel? (I'm done with the exercise...

any thoughts to this question? Give an example of a C^oo (C infinity) function f : R->R which is positive on the interval (-1, 1) and 0 elsewhere

Hi, I've a table of data in the following format: x--> 0.1 3.767 4.395 5.0223 y 0.1 | 1 1.5 2.0 2.0---->z 0.6764 | 1 2.0 2.2 3.599-->z 1.10146 | 2 2.2 2.5 3.686-->z 1.3855 | 2.5...

I have a problem where I need to work out a value of a specific point that lies in the quadrilateral that is formed by four separate points. For each point that makes up the quadrilateral, I know the X and Y coordinates and their value, Z. For the point I am trying to find the value for, I only...

I attached the file. I am up to 1(c). Would the error bound of the interpolation value just be taylor series error term? Thanks

Hello everyone Here is my problem lagrange interpolation polynomial across the points([SIZE="5"]x0,[SIZE="5"]y0),([SIZE="5"]x1,[SIZE="5"]y1) and ([SIZE="5"]x2,[SIZE="5"]y2) is given by [SIZE="5"]y[SIZE="1"]0[SIZE="5"]L[SIZE="1"]0([SIZE="5"]x) +...

In my comp physics class, we've been introduced to both c++ and fortran languages. For instance, for our first assignment, I am not sure how to go about investigating the quality of interpolation points for i.e f(x)=sin(x^2) by using n-point langrange interpolation, where n is an input...

Could someone help me understand why interpolation rather than extrapolation should be used for calibration curves (with the exception of Standard additions). I know that extrapolation is less precise, but the book I've got doesn't over any more than that, and I think I need a little more detail...

If you have two standard 3d, orthogonal matrices representing axes of 3d coordinate systems of the same handedness, is it possible to find the vector about which you would rotate one of the matrices to get the other? If so, this would be a lot more intuitive than quaternions (at least for me)...

I have a 3-D traingle, and the edges are a,b,c. If I want to find a line interpolation at a point in the center, let's say that it's P(x,y)... My equations are \Delta Z = A + Bx + Cy \Delta Z_a = A + Bx_a + Cy_a \Delta Z_b = A + Bx_b + Cy_b \Delta Z_c = A + Bx_c + Cy_c In order to...

I was doing some last minute skimming through my book for my exam tomorrow and panic. Can someone please please tell me about finding the median by interpolation and perhaps an example of how it would could used or asked, i will be forever greatful :cool: yasmin x (i can only find a...

Find a formula to calculate G(n) and it should be a polynomial of degree 4. G(n) = 1/6(0)(0-1)(0-2) + 1/6(1)(1-1)(1-2)+...+1/6(n-1)(n-2)(n-3) I know G(0)=G(1)=G(2)=G(3)=0 G(4)=1 G(5)=1+3 G(6)=1+3+6 G(7)=1+2+3+10 G(8)=1+3+6+10+15 (sum of triangle numbers) What should I do to...