The observed data are given below x 12 3 5 7 y 85.379.5 74.5 67160.5 a)Use...
The observed data are given below X 1 2 3 5 7 y 85.379.5 74.5 67 60.5 a)Use the divided difference table to determine the highest possible order. b)Use Newton's polynomial to determine x=3.5
PLEASE USE PYTHON CODE The points x = -2, 1, 4, -1, 3, -4, y = -1, 2, 59, 4, 24, -53 lie on polynomial. Use the divided difference table of Newton's method to determine the degree of the polynomial.
Given these data: x 1 2 3 5 7 8 f(x) 3 6 19 99 291 444 a) Calculate f(4) using Newton's interpolating polynomials of order 1 through 4. Choose your base points to attain good accuracy. What do your results indicate regarding the order of the polynomial used to generate the data in the table?
Problem 3: The following data is given | * | 12. 23.4 4.8 67 | 33. 245 2.8 a) Write the Lagrange polynomial that passes through the points; then use it calculate the interpolated value of y at x = 5.4. b) Write the polynomial in Newton's form that passes through the points; then use it calculate the interpolated value of y at x = 5.4.
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...
For an nth-order Newton's divided difference interpolating polynomial fn(x), the error of interpolation can be estimated by Rn-| g(xmPX, , xm» ,&J . (x-x-Xx-x.) . . . (x-x.) | , where (xo, f(xo)), (xi, fx)).., (Xn-1, f(xn-1) are data points; g[x-,x,,x-.., x,] is the (n+1)-th finite divided difference. To minimize Rn, if there are more than n+1 data points available for calculating fn(x) using the nth-order Newton's interpolating polynomial, n+1 data points (Xo, f(xo)), (x1, f(x)), , (in, f(%)) should...
please solve question no 5 and 6
05.02.2 The acceleration- time data for a small rocket is given in tabular form below. 5. 20 22 18 24 16 14 12 10 Time (s) Acceleration 106.6 (m/s) 37.1 45.8 56.2 30.1 68.0 80.9 94.1 a) Use Newton's divided difference quadratic polynomial interpolation to find the acceleration at t = 15.5 seconds. Be sure to choose your hase points for good accuracy b) Use the quadratic interpolant of part (a) to find...
USING MATLAB.
For given data, estimate the length when time is at 3.5 seconds and at 13 seconds by utilizing the maximum number of data given, and provide the equation for the best fit curve, and plot the curve against the data. (a) Linear regression method (b) Exponential Function (c) Power Function (d) Saturation Function (e) Polynomial regression (f) Lagrange polynomial (8) Newton's divided-difference polynomial Time (sec) Length (in) 10 17 18 25 28 30 30 10 15 36 38
1. (25 pts) Given the
following start for a Matlab function: function [answer] =
NewtonForm(m,x,y,z) that inputs • number of data points m; •
vectors x and y, both with m components, holding x- and
y-coordinates, respectively, of data points; • location z; and uses
divided difference tables and Newton form to output the value of
the Lagrange polynomial, interpolating the data points, at z.
1. (25 pts) Given the following start for a Matlab function: function [answer] NewtonForm(m.x.yz) that...
PLEASE SOLVE THE WHOLE QUESTION
Numerical method
I. 20 points. USE 3 DECIMAL PLACES IN ALL CALCULATIONS. Given the following data, calculate f(2) using Newton's Interpolating polynomial of order 1, order 2 and order 3. What is the true error in each case if the true value of the function atx2is 507 100 5260 Solution: 20 과 260 Write your final answers in the table shown below: Description O Order 1 Order 2 Order 3 True error, %
I. 20...