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4. Construct the Lagrange interpolating polynomials for the following function, and find a bound for the...
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...
(a) Find the interpolating polynomials to the function f(x) = e-* sin(7x) at x = -1,...
(a) Find the interpolating polynomials to the function f(x) = e-* sin(7x) at x = -1, 0, 1 and 2 using. (1) Lagrange's interpolation formula.
4. For the following table, answer the questions. (1) Find the cubic Newton’s interpolating polynomial using...
4. For the following table, answer the questions.
(1) Find the cubic Newton’s interpolating polynomial using the
first four data points and estimate the function value at x=2.5
with the interpolating polynomial.
(2) Find the quartic Newton’s interpolating polynomial using the
five data points and estimate the function value at x=2.5 with the
interpolating polynomial.
(3) Find the bases functions of Lagrange interpolation, Li(x)
(i=1,2,…,5), and estimate the function value at x=2.5 with the
Lagrange interpolating polynomial.
3 5 1...
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...
Problem 2. Given the data points (xi. yi), with xi 2 02 4 yil 5 1 1.25 find the following interpo...
Problem 2. Given the data points (xi. yi), with xi 2 02 4 yil 5 1 1.25 find the following interpolating polynomials, and use MATLAB to graph both the interpolating polynomials and the data points: a) The piecewise linear Lagrange interpolating polynomialx) b) The piecewise quadratic Lagrange interpolating polynomial q(x) c) Newton's divided difference interpolation pa(x) of degree s 4
Problem 2. Given the data points (xi. yi), with xi 2 02 4 yil 5 1 1.25 find the following...
Problem 5 (programming): Create a MATLAB function named lagrange interp.m to perform interpolation using Lagrange polynomials....
Problem 5 (programming): Create a MATLAB function named lagrange interp.m to perform interpolation using Lagrange polynomials. Download the template for function lagrange interp.m. The tem Plate is in homework 4 folder utl TritonED·TIue function lakes in the data al nodex.xi and yi, as well as the target x value. The function returns the interpolated value y. Here, xi and yi are vectors while x and y are scalars. You are not required to follow the template; you can create the...
Using Lagrange interpolation, find degree two interpolating polynomial if following points are known (0, 1, 5),...
Using Lagrange interpolation, find degree two interpolating polynomial if following points are known (0, 1, 5), (2, 0, −3), (1, 2, 8), (−2, −1, 10), (−1, 0, 5
Using Lagrange interpolation, find degree two interpolating polynomial if following points are known (0, 1, 5),...
Using Lagrange interpolation, find degree two interpolating polynomial if following points are known (0, 1, 5), (2, 0, −3), (1, 2, 8), (−2, −1, 10), (−1, 0, 5) (2,3,1)
πα 5. Let f(x) = cos Find the interpolation polynomials at x = 0,1 by Lagrange...
πα 5. Let f(x) = cos Find the interpolation polynomials at x = 0,1 by Lagrange interpolation.Determine the upper bound for f(x) – P1(x).
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?
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...
(a) Find the interpolating polynomials to the function f(x) = e-* sin(7x) at x = -1, 0, 1 and 2 using. (1) Lagrange's interpolation formula.
4. For the following table, answer the questions.
(1) Find the cubic Newton’s interpolating polynomial using the
first four data points and estimate the function value at x=2.5
with the interpolating polynomial.
(2) Find the quartic Newton’s interpolating polynomial using the
five data points and estimate the function value at x=2.5 with the
interpolating polynomial.
(3) Find the bases functions of Lagrange interpolation, Li(x)
(i=1,2,…,5), and estimate the function value at x=2.5 with the
Lagrange interpolating polynomial.
3 5 1...
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...
Problem 2. Given the data points (xi. yi), with xi 2 02 4 yil 5 1 1.25 find the following interpolating polynomials, and use MATLAB to graph both the interpolating polynomials and the data points: a) The piecewise linear Lagrange interpolating polynomialx) b) The piecewise quadratic Lagrange interpolating polynomial q(x) c) Newton's divided difference interpolation pa(x) of degree s 4
Problem 2. Given the data points (xi. yi), with xi 2 02 4 yil 5 1 1.25 find the following...
Problem 5 (programming): Create a MATLAB function named lagrange interp.m to perform interpolation using Lagrange polynomials. Download the template for function lagrange interp.m. The tem Plate is in homework 4 folder utl TritonED·TIue function lakes in the data al nodex.xi and yi, as well as the target x value. The function returns the interpolated value y. Here, xi and yi are vectors while x and y are scalars. You are not required to follow the template; you can create the...
πα 5. Let f(x) = cos Find the interpolation polynomials at x = 0,1 by Lagrange interpolation.Determine the upper bound for f(x) – P1(x).
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?
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