Determine analytically, what is the maximum error in interpolating the function e2x using 5 equispaced points on [-1,1]? As written e^(2x)
Determine analytically, what is the maximum error in interpolating the function e2x using 5 equispaced points on [-1,1]?
As written e^(2x)
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Determine analytically, what is the maximum error in interpolating the function e2x using 5 equispaced points on [-1,1]? As written e^(2x)
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...
1. Runge's function is written as f(x) = 1 25r2 (a) Develop a plot of this function for the inter...
1. Runge's function is written as f(x) = 1 25r2 (a) Develop a plot of this function for the interval from x =-1 to 1 using Matlab (no submission required). Develop the fourth-order Lagrange interpolating polynomial using equispaced function values corresponding to xi =-1,-0.5, 0, 0.5, and 1. (Note that you first need to determine the (a. ) pairs.) Use the polynomial to estimate f(0.9). (b) What is et? (c) Generate a cubic spline using the five data points from...
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...
for the function f(x)=cos(x) define within [0, pi], what will be the maximum error if f...
for the function f(x)=cos(x) define within [0, pi], what will be the maximum error if f is approximated by 10th and 15th degree interpolating polynomials. Solve this in MatLab
1. Determine the root of function f(x)= x+2x-2r-1 by using Newton's method with x=0.8 and error,...
1. Determine the root of function f(x)= x+2x-2r-1 by using Newton's method with x=0.8 and error, e=0.005. 2. Use Newton's method to approximate the root for f(x) = -x-1. Do calculation in 4 decimal points. Letx=1 and error, E=0.005. 3. Given 7x)=x-2x2+x-3 Use Newton's method to estimate the root at 4 decimal points. Take initial value, Xo4. 4. Find the root of f(x)=x2-9x+1 accurate to 3 decimal points. Use Newton's method with initial value, X=2
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....
Quiz 5. Due Wednesday May 22, 2019. zo- e 1,e, 2-. Give the representation Consider interpolating the function In(x (without developing and 'simplifying in al) of the interpolation po...
Quiz 5. Due Wednesday May 22, 2019. zo- e 1,e, 2-. Give the representation Consider interpolating the function In(x (without developing and 'simplifying in al) of the interpolation polynomial Pa(z) expressed by Without calculating In(2) and P2(2) estimate the absolute error IIn(2) - P2(2)] s?
Quiz 5. Due Wednesday May 22, 2019. zo- e 1,e, 2-. Give the representation Consider interpolating the function In(x (without developing and 'simplifying in al) of the interpolation polynomial Pa(z) expressed by
Without calculating In(2)...
class: numerical analysis I wish if it was written in block letter Sorry I can't read...
class: numerical analysis
I wish if it was written in block letter
Sorry I can't read cursive
= COS Problem 1: Recall that the Chebyshev nodes x4, x1,...,xy are determined on the interval (-1,1] as the zeros of Tn+1(x) = cos((n + 1) arccos(x)) and are given by 2j +10 Xj j = 0,1, ... 1 n+1 2 Consider now interpolating the function f(x) = 1/(1 + x2) on the interval (-5,5). We have seen in lecture that if equispaced...
f(x,y)=〖2x〗^2-12x+y^2-6y+10 (a). Explore the function for local minima and maxima: find critical points and determine the type of extremum. (b). Explore the given function for absolute maximum in th...
f(x,y)=〖2x〗^2-12x+y^2-6y+10 (a). Explore the function for local minima and maxima: find critical points and determine the type of extremum. (b). Explore the given function for absolute maximum in the closed region bounded by the triangle with vertices (0,0), (0,3) and (1,3) (c). Identify if there are any critical points inside the rectangle. (d). Explore the function at each of three borders. (e)Determine absolute maximum and minimum. (f). Find critical points of the given function f(x,y) under the constrain x^2-y^2 x=4x+10
1. .) For the following function f(x)= x4 – 2x - 5 Determine the Inflection Points...
1. .) For the following function f(x)= x4 – 2x - 5 Determine the Inflection Points ONLY 2.. For the given sketch of y = :) Find the intersection points A, B and C. (Do not Estimate!) +2, y=x+2= ii) Determine the shaded area enclosed between the given two curves -*+2, y =x +2
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...
1. Runge's function is written as f(x) = 1 25r2 (a) Develop a plot of this function for the interval from x =-1 to 1 using Matlab (no submission required). Develop the fourth-order Lagrange interpolating polynomial using equispaced function values corresponding to xi =-1,-0.5, 0, 0.5, and 1. (Note that you first need to determine the (a. ) pairs.) Use the polynomial to estimate f(0.9). (b) What is et? (c) Generate a cubic spline using the five data points from...
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...
1. Determine the root of function f(x)= x+2x-2r-1 by using Newton's method with x=0.8 and error, e=0.005. 2. Use Newton's method to approximate the root for f(x) = -x-1. Do calculation in 4 decimal points. Letx=1 and error, E=0.005. 3. Given 7x)=x-2x2+x-3 Use Newton's method to estimate the root at 4 decimal points. Take initial value, Xo4. 4. Find the root of f(x)=x2-9x+1 accurate to 3 decimal points. Use Newton's method with initial value, X=2
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....
Quiz 5. Due Wednesday May 22, 2019. zo- e 1,e, 2-. Give the representation Consider interpolating the function In(x (without developing and 'simplifying in al) of the interpolation polynomial Pa(z) expressed by Without calculating In(2) and P2(2) estimate the absolute error IIn(2) - P2(2)] s?
Quiz 5. Due Wednesday May 22, 2019. zo- e 1,e, 2-. Give the representation Consider interpolating the function In(x (without developing and 'simplifying in al) of the interpolation polynomial Pa(z) expressed by
Without calculating In(2)...
class: numerical analysis
I wish if it was written in block letter
Sorry I can't read cursive
= COS Problem 1: Recall that the Chebyshev nodes x4, x1,...,xy are determined on the interval (-1,1] as the zeros of Tn+1(x) = cos((n + 1) arccos(x)) and are given by 2j +10 Xj j = 0,1, ... 1 n+1 2 Consider now interpolating the function f(x) = 1/(1 + x2) on the interval (-5,5). We have seen in lecture that if equispaced...
1. .) For the following function f(x)= x4 – 2x - 5 Determine the Inflection Points ONLY 2.. For the given sketch of y = :) Find the intersection points A, B and C. (Do not Estimate!) +2, y=x+2= ii) Determine the shaded area enclosed between the given two curves -*+2, y =x +2
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