12 26 14 4. (15 marks) Let f(x)=/2x+1 . Use quadratic Lagrange interpolation based on the...
2019-Numerical Analysis- Quiz-2 1. Let f()-( (a) Use quadratic Lagrange interpolation based on the nodes xo 1, x 2, (given e 2.7183, e 7.3891, e 12.1825) f(1.2). a and x 2.5 to approximate f (1.5) and (b) Use cubic Lagrange interpolation based on the nodes xo=0.5, x1 =1, x2 = 2 and x, = 2.5 to approximate f(1.5) and f(12)
2019-Numerical Analysis- Quiz-2 1. Let f()-( (a) Use quadratic Lagrange interpolation based on the nodes xo 1, x 2, (given...
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
1. Using the Lagrange interpolation polynomial, estimate the value of f(4), knowing that f(-1) = 2; f(0) = 0; f(3) = 4 and f (7) = 7. (6 points)
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...
where x is in radians. Use Guadra tic lagrange interpolation bas ed on the nodles Xo 0.x0.5 and xz-lo to apporimate f(os and fll.2) Construct the Divided- Difference lable basedl an the node xo 1.x- 2,X2-4and x3-t, andl find the Newton Polynomial based on xo, Xiandx xk yk 2 6 5
where x is in radians. Use Guadra tic lagrange interpolation bas ed on the nodles Xo 0.x0.5 and xz-lo to apporimate f(os and fll.2)
Construct the Divided- Difference lable...
3. (30 points) Let f(x) = 1/x and data points Zo = 2, x,-3 and x2 = 4. Note that you can use the abscissae to find the corresponding ordinates (a) (8 points) Find by hand the Lagrange form, the standard form, and the Newton form of the interpolating polynomial p2(x) of f(x) at the given points. State which is which! Then, expand out the Newton and Lagrange form to verify that they agree with the standard form of p2...
Problem 2 Let f(x) = sin 2x and P() be the interpolation polynomial off with degree n at 20,***, Im Show that \,f(z) – P() Sin+1 – 20) (1 - 11). (I – In).
Let f(x) be a quadratic function such that f(0)=?4 and
?f(x)/x2(x+3)^6dx is a rational function.
Let f(x)| be a quadratic function such that f(0) = -4| and integral f(x) / x^2(x + 3)^6 dx| is a rational function. Determine the value of f'(0)|.
QUESTION 5: f(x) = 2 -(x-1) + x(x + 1) – 2x(x + 1)(x - 1) + 2x(x + 1)(x - 1)(x - 2) function (-1,2), (0,1), (1,2), (2, -7), (3,10) passes through these points and (4,5) Find the interpolation polynomial that passes through the point. 그 QUESTION 6: f(x) = cosx + x3 + xe-* using the values you want for this function write the second Lagrange interpolation polynomial that cuts and using this polynomial f(1,5) value find the...
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)