Question

In: Computer Science

(a) [10%] Determine the polynomial interpolant to the data t 1 2 3 4 y 11...

(a) [10%] Determine the polynomial interpolant to the data t 1 2 3 4 y 11 29 65 125 using the monomial basis. (b) [10%] Determine the Lagrange polynomial interpolant to the same data and show that the resulting polynomial is equivalent to that obtained in part (a). (c) [30%] Compute the Newton polynomial interpolant to the same data using each of the three methods discussed in class (triangular matrix, incremental interpolation, and divided differences) and show that each produces the same result as the previous two methods.

For part (c) cab you show me the incremental interpolation please !!!

Solutions

Expert Solution

Given is the solution for the problem.

Comment in case of any doubts.


Related Solutions

Consider the following data. 15,−4,−10,8,14,−10,−2,−11 Step 1 of 3: Determine the mean of the given data...
Consider the following data. 15,−4,−10,8,14,−10,−2,−11 Step 1 of 3: Determine the mean of the given data Step 2 of 3: Determine the median of the given data. Step 3 of 3: Determine if the data set is unimodal, bimodal, multimodal, or has no mode. Identify the mode(s), if any exist. Separate multiple modes with commas, if necessary.
Solve equations 1.) y'-y=t/y 2.) y'-(1/t)y=y2sin(t) 3.) y'+y=y2cos(t) 4.) y'-2y=cos(t)/(y1/2)
Solve equations 1.) y'-y=t/y 2.) y'-(1/t)y=y2sin(t) 3.) y'+y=y2cos(t) 4.) y'-2y=cos(t)/(y1/2)
Find the critical numbers of the function. 1. g(y) = (y-1)/(y^2-y+1) 2. h(t) = t^3/4 -...
Find the critical numbers of the function. 1. g(y) = (y-1)/(y^2-y+1) 2. h(t) = t^3/4 - 2t^1/4 3. F(x) = (x^4/5)*(x-4)^2 4. f(x) = 2cos(x)+sin^2(x)
Determine whether it is linear or nonlinear system: 1. y(t) = 3 + x(2t) 2. y(t)...
Determine whether it is linear or nonlinear system: 1. y(t) = 3 + x(2t) 2. y(t) = x(4t) 3. y(t) = -4t[x(2t)] 4. y(t) = e^2[x(2t)] 5. y(t) = x^5(t) 6. y(t) = cost[x(2t)]
y x1 x2 13 20 3 1 15 2 11 23 2 2 10 4 20...
y x1 x2 13 20 3 1 15 2 11 23 2 2 10 4 20 30 1 15 21 4 27 38 0 5 18 2 26 24 5 1 16 2 A manufacturer recorded the number of defective items (y) produced on a given day by each of ten machine operators and also recorded the average output per hour (x1) for each operator and the time in weeks from the last machine service (x2). a. What is the...
A set of data has the following coordinates t 0 1 3 4 7 y 2...
A set of data has the following coordinates t 0 1 3 4 7 y 2 4 5 7 10 a) Find the least-squares fit to this data by a linear function of t (that is, find constants c1,c0 so that y(t) = c1t + c0 is the best linear fit to this set of data). b) Find the equation of the best quadratic fit to the same set of data. Then find the equation of the polynomial of smallest...
2. Consider the following data: x= 1, 2, 3, 4, 5 y =3, 2, 4, 6,...
2. Consider the following data: x= 1, 2, 3, 4, 5 y =3, 2, 4, 6, 5 By hand, not using Matlab, and showing your work: (a) Compute the correlation coefficient. (b) Find the least-squares line. (c) Find the standard deviation around the least-squares line.
1. Consider the initial value problem y′ =1+y/t, y(1)=3 for1≤t≤2. • Show that y(t) = t...
1. Consider the initial value problem y′ =1+y/t, y(1)=3 for1≤t≤2. • Show that y(t) = t ln t + 3t is the solution to the initial value problem. • Write a program that implements Euler’s method and the 4th order Runke-Kutta method for the above initial value problem. Use your program to solve with h = 0.1 for Euler’s and h = 0.2 for R-K. • Include a printout of your code and a printout of the results at each...
y' = 2 + t^2 + y^2 0<t<1 y(0)=0 use the euler method to determine step...
y' = 2 + t^2 + y^2 0<t<1 y(0)=0 use the euler method to determine step size (h) to keep global truncation error below .0001
Consider the following time series data. t 1 2 3 4 5 6 7 yt 10...
Consider the following time series data. t 1 2 3 4 5 6 7 yt 10 9 7 8 6 4 4 a. Construct a time series plot. What type of pattern exists in the data? b. Develop the linear trend equation for this time series. c. What is the forecast for t=8?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT