MTH603 Quiz 2 Solution and Discussion

Forthegivendatapoints(4,45),(5,104),and(6,190),thezero−orderdividedifferencewillbe

For the following data

Whichofthefollowingmethodcanbeusedforinterpolationforthegivenvaluesofxandy?x y0.30.0670.70.2480.90.518
Lagrangens interpolation

If y(x) is approximated by a polynomial Pn(x) of degree n then the error is given by
ε(x)=y(x)+Pn(x)
ε(x)=y(x)−Pn(x)
ε(x)=y(x)×Pn(x)
ε(x)=y(x)÷Pn(x) 
@zaasmi said in MTH603 Quiz 2 Solution and Discussion:
Forthegivendividedifferencetablex 1 4 7y2.23.54.11stD.D0.43330.22ndD.D−0.0389theNewton′sdividedifferenceinterpolationformulawillbe
y=f(x)=2.2+(x−1)(−0.0389)+(x−1)((x−4)(0.4333)
y=f(x)=2.2+(x−1)(0.4333)+(x−1)((x−4)(−0.0389)
y=f(x)=−0.0389+(x−1)(0.4333)+(x−1)((x−4)(2.2)
y=f(x)=−0.0389+(x−1)(2.2)+(x−1)((x−4)(0.4333)
Solution:

Forthegivendividedifferencetablex 1 4 7y2.23.54.11stD.D0.43330.22ndD.D−0.0389theNewton′sdividedifferenceinterpolationformulawillbe
y=f(x)=2.2+(x−1)(−0.0389)+(x−1)((x−4)(0.4333)
y=f(x)=2.2+(x−1)(0.4333)+(x−1)((x−4)(−0.0389)
y=f(x)=−0.0389+(x−1)(0.4333)+(x−1)((x−4)(2.2)
y=f(x)=−0.0389+(x−1)(2.2)+(x−1)((x−4)(0.4333)

Whatwillbethevalueof′a′inthegivendividedifferencetable? x2468y0.51.11.72…21stD.D0.30.30.252ndD.Da−0.01253rdD.D−0.0021

@zaasmi said in MTH603 Quiz 2 Solution and Discussion:
For the given data points (1,0.3),(3,1),and(5,1.2) the divide difference table will be given as
Forthegivendatapoints(1,0.3),(3,1),and(5,1.2)thedividedifferencetablewillbegivenas

For the given data points (1,0.3),(3,1),and(5,1.2) the divide difference table will be given as


Δ= ?

In Lagrange’s interpolation, for the given five points we can represent the function f (x) by a polynomial of degree
3
4
5
6 
In Simpson’s 1/3 rule, the global error is of ………………
O(h2)
O(h3)
O(h4)
None of the given choices 
Integration is a ………………process.
Subtracting
Summing
Dividing
None of the given choices 
Which of the following is the Richardson’s Extrapolation limit: F1(h/2) provided that F(h/2) = F(h) = 1 ?
0
1
3
4 
In the process of Numerical Differentiation, we differentiate an interpolating polynomial in place of .
actual function
extrapolating polynomial
Lagrange’s polynomial
Newton’s Divided Difference Interpolating polynomial