Using Lagrange interpolation, find degree two interpolating polynomial if following points are known (0, 1, 5),...

Question

Question

Using Lagrange interpolation, find degree two interpolating polynomial if following points are known (0, 1, 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

math Advanced-Math

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Answer:- Given points are 10,1,5), (2,0,-3), 62,-1,10), 1-1,0,5),(1,2,81 so two set of point. are (0,1). 12,0), (2,-)) ,(-1, (82_2x) (211 x 10 (x2+2x) (321) Br(e) = 6x3y) (221) X5 t 4 Lagrange interpolating for point set er Similiar way. X(-3) + 8x3

Add a comment

Answer 2

Similar Homework Help Questions

Using Lagrange interpolation, find degree two interpolating polynomial if following points are known (0, 1, 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...

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...
Problem 2. Given the data points (xi. yi), with xi 2 02 4 yil 5 1 1.25 find the following interpo...

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...

12. Given the data set: We want to find the interpolating polynomial of degree 2 through...

12. Given the data set: We want to find the interpolating polynomial of degree 2 through these points. a) Write the interpolating polynomial in Lagrange form b) Write the interpolating polynomial in Newton form.
3) A 2nd-order Lagrange Interpolating Polynomial is to be fit to the following data points:(1)-1,1(2)4, 1(3)-9....

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)
Polynomial Interpolation Determine analytically, what is the maximum error in interpolating the function e2x using 5 equispaced points on [-1,11? . Compare this with the upper bound using the 5 roots...

Polynomial Interpolation Determine analytically, what is the maximum error in interpolating the function e2x using 5 equispaced points on [-1,11? . Compare this with the upper bound using the 5 roots of T5(x) to interpolate e2* Construct and plot the actual pointwise interpolation error (by sampling at lots of points). Are either of your error bounds close? Polynomial Interpolation Determine analytically, what is the maximum error in interpolating the function e2x using 5 equispaced points on [-1,11? . Compare this...

1. Using the Lagrange interpolation polynomial, estimate the value of f(4), knowing that f(-1) = 2;...

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)
(a) Find the degree 1 interpolating P(x) through the points (a, f(a)) and (b, f(b)) (b) Develop the following formula b...

(a) Find the degree 1 interpolating P(x) through the points (a, f(a)) and (b, f(b)) (b) Develop the following formula by using the interpolating polynomial P1 (x), (c) Find the degree of precision of the approximation, T1 (f) = f(1) + f(-1), for f(r)dr. (a) Find the degree 1 interpolating P(x) through the points (a, f(a)) and (b, f(b)) (b) Develop the following formula by using the interpolating polynomial P1 (x), (c) Find the degree of precision of the approximation,...
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 divi...

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...

**********************matlab code please******************* 1. Interpolation error of polynomial fit Using 11 equi-dist...

**********************matlab code please******************* 1. Interpolation error of polynomial fit Using 11 equi-distributed points (10 equal segments) in the interval [-1 1], Using Newton's form find and plot the interpolating polynomial p(x) for the function f(x) -1/(125x2). Comment on the large discrepancies between p(x) and the function f(x) that the data came from Write down an expression for the error in the interpolating polynomial above? Which part of the expression is responsible for the large errors observed? 1. Interpolation error of...

Using Lagrange interpolation, find degree two interpolating polynomial if following points are known (0, 1, 5),...

Homework Answers