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. 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...
3) A 2nd-order Lagrange Interpolating Polynomial is to be fit to the following data points:(1)-1,1(2)4, 1(3)-9. Determine the polynomial term corresponding to the data point f(3) 8. Be sure to simplify as much as possible. (Don't take time to write the other two terms.) (1 point)
Let (xi , f(xi)), i = 0, . . . , 3, be data points, where xi = i + 2, for i = 0, . . . , 3. Given the divided differences f[x0] = 1, f[x0, x1] = 2, f[x0, x1, x2] = −7, f[x0, x1, x2, x3] = 9, add the data point (0, 3), find a Newton form for the Lagrange polynomial interpolating all 5 data points. 3. (25 pts) Let (r,, f()), 0,3, be data...
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...
3. Consider the function f(x) = cos(x) in the interval [0,8]. You are given the following 3 points of this function: 10.5403 2 -0.4161 6 0.9602 (a) (2 points) Calculate the quadratic Lagrange interpolating polynomial as the sum of the Lo(x), L1(x), L2(x) polynomials we defined in class. The final answer should be in the form P)a2 bx c, but with a, b, c known. DELIVERABLES: All your work in constructing the polynomial. This is to be done by hand...
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?
1)Select five-data pair (x, y) randomly yourself (not from any books, any documents etc. Form yourself!) and - Fit a curve with a linear equation. - Fit a curve with non-linear equation by writing the equation in a linear form. - Fit a curve with fourth-order polynomial directly. - Find fourth-order polynomial by Lagrange interpolating polynomial method. - Find fourth-order polynomial by Newton's interpolating polynomial method. Numerical methods.
please help with #1 a and b. thank you Use the following data for all problems: The data below defines the sea-level concentration of dissolved oxygen for fresh water as a function of temperature: T°C omg/L 0 8 16 14.621 11.843 9.870 24 32 40 8.418 7.305 6.413 a. Approximate o(19) using a 1st order Newton's interpolating polynomial. b. Approximate o(19) using a 2nd order Newton's interpolating polynomial. 2) Use linear algebra to find the coefficients of the 2nd order...
8396 5101281 5 8 2 0 1 12 ( 4 2 1 ) ) ) 0000 f-000 0246802 (i) Defining fo-f(zo). Л that the quadratic f(x) and f2 f(x2), where Zo-x1-h and x2-xuth, show 2 , f2 - jo 2h2 2h is the quadratic interpolating function for fo, fı and f2 (i.e. show that p(x)-f) 4] (ii) Use the interpolating polynomial p(x) as defined above, with Zo-12, xỉ-1.4 and 22 -1.6 (and fo, fı and f2 given by the table...