Homework Answers
Procedure is very long, if you have studied then you would be knowing basic procedure for natural cubic spline. I have used software for answer.
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3) Use Spline interpolation method for smoothing of the given data points. Note you have four...
matlab D [10 pts Consider following data points Groups a) Use linear interpolation method to fit...
matlab
D [10 pts Consider following data points Groups a) Use linear interpolation method to fit data. Use 'interp1 b) Fit data with a cubie spline. Use "spline e) Fit a 4h degree polynomial using "polyf Tools Help Make a figure for each of the interpolation methods. In each figure show data points using ocircle marks, a curve that eorresponds to the interpolation method
3D Cubic B-Spline Interpolation and Error Estimation Theme: Implement and study 3D Cubic Spline ...
3D Cubic B-Spline Interpolation and Error Estimation Theme: Implement and study 3D Cubic Spline Interpolation Input: a set of points in 3D space (data(x,y,z)) Output: Spline, Spline data points and error, 3D graph that shows the original points and the Spline The major steps involved in the B-Spline Fitting and Error Estimation are as mentioned below: 1- Sample the data points from input data. 2- Interpolate to find the position of control points. 3- Use the B-Spline basis function to...
interp1, polyfit, polyval, diff, trap, quad 1 INTERPOLATION (2 PTS) You did an experiment and obtained the followin...
interp1, polyfit, polyval, diff, trap, quad 1 INTERPOLATION (2 PTS) You did an experiment and obtained the following data set 90 x 10 20 30 60 70 80 100 60 82 111 140 167 198 200 220 Y 23 45 Create the x and y vectors to represent the above data and use the interpl command to find the interpolation result for the following questions 1. Use linear interpolation to approximate the value of y when x=15 2. Use cubic...
matlab matlab For this problem you will test a few interpolation approaches for the application of generating interpolated data. We'll do this by interpolating data that is sampled from a k...
matlab
matlab
For this problem you will test a few interpolation approaches for the application of generating interpolated data. We'll do this by interpolating data that is sampled from a known mathematical function. The same function can then be used to compute true values at the interpolated points to use in error Consider the following mathematical function (Runge's function): 1+25r2 Write a function mfile that uses this formula to generate a set of data use those points along approaches outlined...
QUESTION 4 (a) A natural cubic spline that fits the data given by f(3.0) = -5.6790,...
QUESTION 4 (a) A natural cubic spline that fits the data given by f(3.0) = -5.6790, F (3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline. (b) Consider the nonlinear system x2 + y = 9, 22 + y2 = 25, x, y > 0. Perform one iteration of Newton's method to approximate the solution, starting with (2, 4) as...
3. (30 points) Let f(x) = 1/x and data points Zo = 2, x,-3 and x2 = 4. Note that you can use the ...
3. (30 points) Let f(x) = 1/x and data points Zo = 2, x,-3 and x2 = 4. Note that you can use the abscissae to find the corresponding ordinates (a) (8 points) Find by hand the Lagrange form, the standard form, and the Newton form of the interpolating polynomial p2(x) of f(x) at the given points. State which is which! Then, expand out the Newton and Lagrange form to verify that they agree with the standard form of p2...
Interpolation Polynomial Coding MATlab
I have to write a Matlab function called "interpoly(x,y) which calculates the corresponding interpolation polynomial for given support points (xj,fj) with x=[x1,x2,...,xn] and f=[f1,f2,...,fn] and in interval x[min xj, max xj] plotted. Any method can be used to calculate the interpolation polynomial but I think Lagrange would be the best. One rule is that I can not use "polyfit" command.I have to test the programm with values of fj of the functions f(x)=cos(x) and f(x)=1/(1+x^2) each in the interval [-6,6]....
1. Given the data table with f(x) = yn for a unkown function f, determine the...
1. Given the data table with f(x) = yn for a unkown function f, determine the cubic spline interpolation that intersects with the 3 data points. No need to solve for the coefficients. Just set up the eight equations. 1.1 3.5 1.2 3.7 1.3 2.9 2. The fixed point iteration can be used to find the solution of a function f(r) = 0. To use this method, we need to first identify g(x) such that the solution of g(x) =...
Question 3 (a) Grven that f(-2)= 46, f(-1) 4, J(1) 1, f(3)= 156, and f(4)= 484, formula to estimate f(0) Use four-d...
Question 3 (a) Grven that f(-2)= 46, f(-1) 4, J(1) 1, f(3)= 156, and f(4)= 484, formula to estimate f(0) Use four-decimal arithmetac with rounding use the Lagrange interpolation (8) (b) Why should the Lagrange formula be used in practice only with caution" (2) (e) Wnte down the system of equations that need to be solved in order Function for the following data to construct the natural cubic spline 30 -5 6790 -3 6674 3 1 32-22178 (8) Note You...
matlab 2) Plots the individual points with "star" marks b) Fisa cubie spline to the data...
matlab
2) Plots the individual points with "star" marks b) Fisa cubie spline to the data use "o" marks c) Fits a 5th order polynomial use "x" marks 3) MATLAB contains functions to calculate the natural logarithm (log), the logarithm to the base 10 (log 10), and the logarithm to the buse 2 (log2). However, if you want to find a logarithm to another base for example, base - you'll have to do the math yourself with the formula log)(x)...
matlab
D [10 pts Consider following data points Groups a) Use linear interpolation method to fit data. Use 'interp1 b) Fit data with a cubie spline. Use "spline e) Fit a 4h degree polynomial using "polyf Tools Help Make a figure for each of the interpolation methods. In each figure show data points using ocircle marks, a curve that eorresponds to the interpolation method
interp1, polyfit, polyval, diff, trap, quad 1 INTERPOLATION (2 PTS) You did an experiment and obtained the following data set 90 x 10 20 30 60 70 80 100 60 82 111 140 167 198 200 220 Y 23 45 Create the x and y vectors to represent the above data and use the interpl command to find the interpolation result for the following questions 1. Use linear interpolation to approximate the value of y when x=15 2. Use cubic...
matlab
matlab
For this problem you will test a few interpolation approaches for the application of generating interpolated data. We'll do this by interpolating data that is sampled from a known mathematical function. The same function can then be used to compute true values at the interpolated points to use in error Consider the following mathematical function (Runge's function): 1+25r2 Write a function mfile that uses this formula to generate a set of data use those points along approaches outlined...
QUESTION 4 (a) A natural cubic spline that fits the data given by f(3.0) = -5.6790, F (3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline. (b) Consider the nonlinear system x2 + y = 9, 22 + y2 = 25, x, y > 0. Perform one iteration of Newton's method to approximate the solution, starting with (2, 4) as...
3. (30 points) Let f(x) = 1/x and data points Zo = 2, x,-3 and x2 = 4. Note that you can use the abscissae to find the corresponding ordinates (a) (8 points) Find by hand the Lagrange form, the standard form, and the Newton form of the interpolating polynomial p2(x) of f(x) at the given points. State which is which! Then, expand out the Newton and Lagrange form to verify that they agree with the standard form of p2...
1. Given the data table with f(x) = yn for a unkown function f, determine the cubic spline interpolation that intersects with the 3 data points. No need to solve for the coefficients. Just set up the eight equations. 1.1 3.5 1.2 3.7 1.3 2.9 2. The fixed point iteration can be used to find the solution of a function f(r) = 0. To use this method, we need to first identify g(x) such that the solution of g(x) =...
Question 3 (a) Grven that f(-2)= 46, f(-1) 4, J(1) 1, f(3)= 156, and f(4)= 484, formula to estimate f(0) Use four-decimal arithmetac with rounding use the Lagrange interpolation (8) (b) Why should the Lagrange formula be used in practice only with caution" (2) (e) Wnte down the system of equations that need to be solved in order Function for the following data to construct the natural cubic spline 30 -5 6790 -3 6674 3 1 32-22178 (8) Note You...
matlab
2) Plots the individual points with "star" marks b) Fisa cubie spline to the data use "o" marks c) Fits a 5th order polynomial use "x" marks 3) MATLAB contains functions to calculate the natural logarithm (log), the logarithm to the base 10 (log 10), and the logarithm to the buse 2 (log2). However, if you want to find a logarithm to another base for example, base - you'll have to do the math yourself with the formula log)(x)...
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