Interpolating Runge's function with Lagrange vs Natural cubic splines
Runges function given by R(x) = 1/1+25x^2.
Solve without using the built in MATLAB functions.
Choose 9 equidistant points on [-1,1] and let yi = R(xi) and draw the points in MATLAB
Interpolate 8th degree Langrange through the points and draw the curve in the same plot as above.
Interpolate natural cubic splines thorugh the points and draw the curve in the same plot.
Determine which method best approximates R(x) by measuring the errors.
Any help is appreciated
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Interpolating Runge's function with Lagrange vs Natural cubic splines
Consider polynomial interpolation of the function f(x)=1/(1+25x^2) on the interval [-1,1] by (1) ...
Consider polynomial interpolation of the function f(x)=1/(1+25x^2) on the interval [-1,1] by (1) an interpolating polynomial determined by m equidistant interpolation points, (2) an interpolating polynomial determined by interpolation at the m zeros of the Chebyshev polynomial T_m(x), and (3) by interpolating by cubic splines instead of by a polynomial. Estimate the approximation error by evaluation max_i |f(z_i)-p(z_i)| for many points z_i on [-1,1]. For instance, you could use 10m points z_i. The cubic spline interpolant can be determined in...
Use cubic splines to represent a curve (x(s), y(s)) that is in the shape of the...
Use cubic splines to represent a curve (x(s), y(s)) that is in the shape of the script letter L below. List the points you used to make the splines, and make a plot of your curve. You may use the provided grid to estimate the nodes by hand, or use software to help identify points on the curve. For example, in MATLAB the commands imread, image, and ginput could be used to aid in selecting your points.
Matlab Matlab Matlab Matlab, Please solve this problem Problem 4 : Runge's phenomenon For this proble,...
Matlab Matlab Matlab Matlab, Please solve this problem
Problem 4 : Runge's phenomenon For this proble, you wil interpolate the function h(x) = tanh(10x) in I [a, b, through n datapoints (xi, hx with equidistant nodes for several values of n, and observe the behavior of the interpolating polynomial as n increases. You should use the pair of functions polyfit and polyval In your prob40: (a) Interpolate the function tanh(10x) in [-1,1] using a uniform grid of n nodes, where...
2. Consider interpolating the data (x0,yo), . . . , (x64%) given by Xi | 0.1...
2. Consider interpolating the data (x0,yo), . . . , (x64%) given by Xi | 0.1 | 0.15 | 0.2 | 0.3 | 0.35 | 0.5 | 0.75 yi 4.0 1.0 1.22.12.02.52.5 For all tasks below, please submit your MATLAB code and your plots. You can write all code in a single (a) Using MATLAB, plot the interpolating (6th degree) polynomial given these data on the domain .m-file [0.1,0.75] using the polyfit and polyval commands. To learn how to use...
I need help with parts A B D E and F. Please show hand work for...
I need help with parts A B D E and F. Please show hand work
for solving A and B while D and E should be matlab codes. How do i
pick the right graph for part F?
5 2 4 6 Linear spline: s fi+ (x-x) 2) Given the points 40 78 125 256 348 425 X1-x a) Write the correct linear spline equation to interpolate for x 4.72, simplifying where appropriate to get to the slope-intercept form. (4...
Use cubic splines to represent a curve (x(s), y(s)) that is in the shape of the script letter L below. List the points you used to make the splines, and make a plot of your curve. You may use the provided grid to estimate the nodes by hand, or use software to help identify points on the curve. For example, in MATLAB the commands imread, image, and ginput could be used to aid in selecting your points.
Matlab Matlab Matlab Matlab, Please solve this problem
Problem 4 : Runge's phenomenon For this proble, you wil interpolate the function h(x) = tanh(10x) in I [a, b, through n datapoints (xi, hx with equidistant nodes for several values of n, and observe the behavior of the interpolating polynomial as n increases. You should use the pair of functions polyfit and polyval In your prob40: (a) Interpolate the function tanh(10x) in [-1,1] using a uniform grid of n nodes, where...
2. Consider interpolating the data (x0,yo), . . . , (x64%) given by Xi | 0.1 | 0.15 | 0.2 | 0.3 | 0.35 | 0.5 | 0.75 yi 4.0 1.0 1.22.12.02.52.5 For all tasks below, please submit your MATLAB code and your plots. You can write all code in a single (a) Using MATLAB, plot the interpolating (6th degree) polynomial given these data on the domain .m-file [0.1,0.75] using the polyfit and polyval commands. To learn how to use...
I need help with parts A B D E and F. Please show hand work
for solving A and B while D and E should be matlab codes. How do i
pick the right graph for part F?
5 2 4 6 Linear spline: s fi+ (x-x) 2) Given the points 40 78 125 256 348 425 X1-x a) Write the correct linear spline equation to interpolate for x 4.72, simplifying where appropriate to get to the slope-intercept form. (4...
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