1. Using the Lagrange interpolation polynomial, estimate the value of f(4), knowing that f(-1) = 2;...
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), (2, 0, −3), (1, 2, 8), (−2, −1, 10), (−1, 0, 5) (2,3,1)
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...
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...
a) Find False Position function for this data. b) Find the third-order interpolation function with Lagrange method c) Find the third-order interpolation function with Newton's Divided Difference Method. d)Find the natural spline interpolation function for the same data e)Draw the given points in a row using the False Position function, the third order polynomial obtained by Lagrange and Newton's Divided Difference Method, and the natural spline interpolation function using MATLAB. 4-0 2
8. Use divided differences to find the interpolation polynomial for the data f (x)-1 -3 -2 4 f' (x) f"(x) 8. Use divided differences to find the interpolation polynomial for the data f (x)-1 -3 -2 4 f' (x) f"(x)
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...
12 26 14 4. (15 marks) Let f(x)=/2x+1 . Use quadratic Lagrange interpolation based on the nodes x, 0, x-1 and x, 2 to approximate f(1.2) 12 26 14 4. (15 marks) Let f(x)=/2x+1 . Use quadratic Lagrange interpolation based on the nodes x, 0, x-1 and x, 2 to approximate f(1.2)
er Lagrange ,Divided difference and Hermitewatnejed, Jnp 1.5, and x2-2, andf (x)ssin(x) * Given the point sx.-1, a) Find its Lagrange interpolation P on these points b) Write its newton's divided difference P, polynomial c)Write Hermite Hs by Using part a outcomes d) Write Hermite Hi by Using part b outcomes Rules: Lagrange form of Hermite polynomial of degre at most 2n-+1 Here, L., (r) denotes the Lagrange coefficient polynomial of degree n. If ec la.bl, then the error formula...
5. Write down the error term E3(x) for cubic Lagrange interpolation to f(x), where interpolation is to be exact at the four nodes xo = -1, x1 = 0, x2 = 3, and x3 = 4 and f(x) is given by (a) f(x) = 4x3 -- 3x + 2 (b) f(x)= x4 - 2x3 (c) f(x) = x3 – 5x4