Compute the quartic interpolating polynomial for the Hermite interpolation problem p(0) = 2, p'(0) = -9...

Compute the quartic interpolating polynomial for the Hermite interpolation problem

p(0) = 2, p'(0) = -9

p(1) = -4, p'(1) = 4

p(2) = 44

with respect to the Newton basis. Compute the divided differences. Find a quintic interpolating polynomial that additionally satisfies p(3) = 2.

Expert Solution

Colby Messinger answered 1 year ago

Consider polynomial interpolation of the function f(x)=1/(1+25x^2) on the interval [-1,1] by (1) an interpolating polynomial...

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...

Find the Chebyshev interpolation nodes on the interval [4,12] for an interpolating polynomial of degree 5

Prove that the algorithm for computing the coefficients in the Newton form of the interpolating polynomial...

Prove that the algorithm for computing the coefficients in the Newton form of the interpolating polynomial involves n^2 long operations (multiplication and division).

Use the Lagrange interpolating polynomial to approximate √3 with the function f(x)= 3x-0.181and the values x0=-2,...

Use the Lagrange interpolating polynomial to approximate √3 with the function f(x)= 3x-0.181and the values x0=-2, X1=-1, X2=0, X3=1 and X4=2.(Uses 4 decimal figures)

solve the inital value problem ?′′ + 6?′ + 9? = 2?^(-t) ; ?(0) =4, ?’(0)...

solve the inital value problem ?′′ + 6?′ + 9? = 2?^(-t) ; ?(0) =4, ?’(0) = −6

build an excel sheet to calculate the coefficients of the third order Newton interpolating polynomial,and solve...

build an excel sheet to calculate the coefficients of the third order Newton interpolating polynomial,and solve it for any point x, please solve it by excel and i need the file thanks in advance

Find a polynomial p(x) with zeroes at 1,-2, and -1 and such that p(2) equals 6...

Find a polynomial p(x) with zeroes at 1,-2, and -1 and such that p(2) equals 6 ? What is the remainder when the polynomial p(x) equals (x^101 - x^50 - 3x^9 + 2) is divided by (x+1) ? Find a polynomial of degree 4 with zeroes at -2, 9, and 5. (NOTE: leave your polynomial factored; please do not expand it) Factor the polynomial x^3 - 4x^2 + 3x + 2. List all the possible rational roots of the polynomial...

Find the lagrange polynomials that approximate f(x) = x3 a ) Find the linear interpolation polynomial...

Find the lagrange polynomials that approximate f(x) = x3 a ) Find the linear interpolation polynomial P1(x) using the nodes x0= -1 and x1 = 0 b) Find the quadratic interpolation polynomial P2(x) using the nodes x0= -1 and x1 = 0 and x2 = 1 c) Find the cubic interpolation polynomial P3(x) using the nodes x0= -1 and x1 = 0 and x2 = 1 and x3=2 d) Find the linear interpolation polynomial P1(x) using the nodes x0= 1...

Use Lagrange interpolation to find the polynomial p3(x) of degree 3 or less, that agree with...

Use Lagrange interpolation to find the polynomial p3(x) of degree 3 or less, that agree with the following data: p3(−1) = 3, p3(0) = −4, p3(1) = 5, and p3(2) = −6. Using python to solve

compute the 2-degree polynomial approximation of f(x)= 3x-e^x^2

Question