**********************matlab code please*******************
![1. Interpolation error of polynomial fit Using 11 equi-distributed points (10 equal segments) in the interval [-1 1], Using N](http://img.homeworklib.com/images/552f5d4f-0eaf-4e9a-be59-a8d01d3a4237.png?x-oss-process=image/resize,w_560)
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**********************matlab code please******************* 1. Interpolation error of polynomial fit Using 11 equi-dist...
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...
Polynomial Interpolation Determine analytically, what is the maximum error in interpolating the function e2x using 5 equispaced points on [-1,11? . Compare this with the upper bound using the 5 roots...
Polynomial Interpolation Determine analytically, what is the maximum error in interpolating the function e2x using 5 equispaced points on [-1,11? . Compare this with the upper bound using the 5 roots of T5(x) to interpolate e2* Construct and plot the actual pointwise interpolation error (by sampling at lots of points). Are either of your error bounds close?
Polynomial Interpolation Determine analytically, what is the maximum error in interpolating the function e2x using 5 equispaced points on [-1,11? . Compare this...
For an nth-order Newton's divided difference interpolating polynomial fn(x), the error of interpolation can be estimated by Rn-| g(xmPX, , xm» ,&J . (x-x-Xx-x.) . . . (x-x.) | , where (xo, f(...
For an nth-order Newton's divided difference interpolating polynomial fn(x), the error of interpolation can be estimated by Rn-| g(xmPX, , xm» ,&J . (x-x-Xx-x.) . . . (x-x.) | , where (xo, f(xo)), (xi, fx)).., (Xn-1, f(xn-1) are data points; g[x-,x,,x-.., x,] is the (n+1)-th finite divided difference. To minimize Rn, if there are more than n+1 data points available for calculating fn(x) using the nth-order Newton's interpolating polynomial, n+1 data points (Xo, f(xo)), (x1, f(x)), , (in, f(%)) should...
Please use matlab, post the code, and dont just write the code by hand. Thank you!...
Please use matlab, post the code, and dont just write
the code by hand. Thank you!
4 [3 points] Use the function f(x on the interval [5, 5] and the 11 points below to find a N-10 Lagrange polynomial, using MATLAB. You will need to write code for and plot the polynomial as a function of x, but you do not have to write the polynomials down by hand 5 0 2 3 4 5 f(x) | 0.0399 | 00623...
How do your write this in Matlab. Create a program that takes as input: An integer...
How
do your write this in Matlab.
Create a program that takes as input: An integer nFunction that is either 1 or 2 indicating which of the two functions below to nsc * An integer n in [1.oc) indicating how many data points (ro."). ·The left endpoint a of an overall interval. (n泓) tote. The right endpoint b of an overall interval Your program should find the interpolating polynomial of degree less than or equal to of the requested function...
Compute, using divided differences, the value of the piecewise cubic Her- mite interpolating polynomial at x = 11=10 giv...
Compute, using divided differences, the value of the piecewise
cubic Her-
mite interpolating polynomial at x = 11=10 given nodes at xi = i,
for i = 1; : : : ; 10,
and values and derivatives at the nodes from the function f(x) =
1=x.
Remember iterative formula for divided differences:
2. (25 pts) Compute, using divided differences, the value of the piecewise cubic Her mite interpolating polynomial at x-11/10 given nodes at ai-i, for i-1, , 10. and...
this is numerical analysis 2. Consider the function f(x) = -21° +1. (a) Calculate the interpolating...
this is numerical analysis
2. Consider the function f(x) = -21° +1. (a) Calculate the interpolating polynomial pz() for data using the nodes 2o = -1, 11 = 0, 12 = 1. Simplify the polynomial to standard form. Use the error theorem for polynomial interpolation to bound the error f(x) - P2(x) on the interval (-1,2). Is this bound realistic?
matlab The error function is a mathematical function that frequently arises in probability and statistics. It also c...
matlab
The error function is a mathematical function that frequently arises in probability and statistics. It also can show up in the solution to some partial differential equations, particularly those arising in heat and mass transfer applications. The error function is defined as 2 e-t dt picture attached This function is actually built-in to MATLAB as the command erf, and here we'll use that function to compute a "true value" with which we can compare results of two interpolation approaches....
Consider the function f(x) 1 25x which is used to test various interpolation methods. For the rem...
Consider the function f(x) 1 25x which is used to test various interpolation methods. For the remainder of this problem consider only the interval [-1, 1] The x-values for the knots (or base-points) of the interpolation algorithm are located at x--1,-0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75 1. (a) Create a "single" figure in Matlab that contains 6 subplots (2x3) and is labelled as figure (777), i.e the figure number is 777. Plot in each subplot the function f(x) using...
1. Consider the polynonial Pl (z) of degree 4 interpolating the function f(x) sin(x) on the interval n/4,4 at the e...
1. Consider the polynonial Pl (z) of degree 4 interpolating the function f(x) sin(x) on the interval n/4,4 at the equidistant points r--r/4, xi =-r/8, x2 = 0, 3 π/8, and x4 = π/4. Estimate the maximum of the interpolation absolute error for x E [-r/4, π/4 , ie, give an upper bound for this absolute error maxsin(x) P(x) s? Remark: you are not asked to give the interpolation polynomial P(r).
1. Consider the polynonial Pl (z) of degree 4...
Polynomial Interpolation Determine analytically, what is the maximum error in interpolating the function e2x using 5 equispaced points on [-1,11? . Compare this with the upper bound using the 5 roots of T5(x) to interpolate e2* Construct and plot the actual pointwise interpolation error (by sampling at lots of points). Are either of your error bounds close?
Polynomial Interpolation Determine analytically, what is the maximum error in interpolating the function e2x using 5 equispaced points on [-1,11? . Compare this...
For an nth-order Newton's divided difference interpolating polynomial fn(x), the error of interpolation can be estimated by Rn-| g(xmPX, , xm» ,&J . (x-x-Xx-x.) . . . (x-x.) | , where (xo, f(xo)), (xi, fx)).., (Xn-1, f(xn-1) are data points; g[x-,x,,x-.., x,] is the (n+1)-th finite divided difference. To minimize Rn, if there are more than n+1 data points available for calculating fn(x) using the nth-order Newton's interpolating polynomial, n+1 data points (Xo, f(xo)), (x1, f(x)), , (in, f(%)) should...
Please use matlab, post the code, and dont just write
the code by hand. Thank you!
4 [3 points] Use the function f(x on the interval [5, 5] and the 11 points below to find a N-10 Lagrange polynomial, using MATLAB. You will need to write code for and plot the polynomial as a function of x, but you do not have to write the polynomials down by hand 5 0 2 3 4 5 f(x) | 0.0399 | 00623...
How
do your write this in Matlab.
Create a program that takes as input: An integer nFunction that is either 1 or 2 indicating which of the two functions below to nsc * An integer n in [1.oc) indicating how many data points (ro."). ·The left endpoint a of an overall interval. (n泓) tote. The right endpoint b of an overall interval Your program should find the interpolating polynomial of degree less than or equal to of the requested function...
Compute, using divided differences, the value of the piecewise
cubic Her-
mite interpolating polynomial at x = 11=10 given nodes at xi = i,
for i = 1; : : : ; 10,
and values and derivatives at the nodes from the function f(x) =
1=x.
Remember iterative formula for divided differences:
2. (25 pts) Compute, using divided differences, the value of the piecewise cubic Her mite interpolating polynomial at x-11/10 given nodes at ai-i, for i-1, , 10. and...
this is numerical analysis
2. Consider the function f(x) = -21° +1. (a) Calculate the interpolating polynomial pz() for data using the nodes 2o = -1, 11 = 0, 12 = 1. Simplify the polynomial to standard form. Use the error theorem for polynomial interpolation to bound the error f(x) - P2(x) on the interval (-1,2). Is this bound realistic?
matlab
The error function is a mathematical function that frequently arises in probability and statistics. It also can show up in the solution to some partial differential equations, particularly those arising in heat and mass transfer applications. The error function is defined as 2 e-t dt picture attached This function is actually built-in to MATLAB as the command erf, and here we'll use that function to compute a "true value" with which we can compare results of two interpolation approaches....
Consider the function f(x) 1 25x which is used to test various interpolation methods. For the remainder of this problem consider only the interval [-1, 1] The x-values for the knots (or base-points) of the interpolation algorithm are located at x--1,-0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75 1. (a) Create a "single" figure in Matlab that contains 6 subplots (2x3) and is labelled as figure (777), i.e the figure number is 777. Plot in each subplot the function f(x) using...
1. Consider the polynonial Pl (z) of degree 4 interpolating the function f(x) sin(x) on the interval n/4,4 at the equidistant points r--r/4, xi =-r/8, x2 = 0, 3 π/8, and x4 = π/4. Estimate the maximum of the interpolation absolute error for x E [-r/4, π/4 , ie, give an upper bound for this absolute error maxsin(x) P(x) s? Remark: you are not asked to give the interpolation polynomial P(r).
1. Consider the polynonial Pl (z) of degree 4...
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