Let f(x) = x sin (2x) – x², xo = 0, x1 = 0.3, X2 = 0.7. - %3D (a) Find Lagrange interpolating polynomial for f(x) using the three given nodes leaving all coefficients correct to 5 decimal places. (b) Using the nodes xo and x1, construct the Hermite interpolating polynomial H3(x) for f(x) using the Lagrange coefficient polynomials expressing all coefficients correct to 5 decimal places.
Let f(x) = x sin (2x) – x², xo = 0, x1 = 0.3, X2 = 0.7. - %3D (a) Find Lagrange interpolating polynomial for f(x) using the three given nodes leaving all coefficients correct to 5 decimal places. (b) Using the nodes xo and x1, construct the Hermite interpolating polynomial H3(x) for f(x) using the Lagrange coefficient polynomials expressing all coefficients correct to 5 decimal places.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
3.please help
Transcribed Image Text:Let f(x) = x sin (2x) – x², xo = 0,
X1 = 0.3,
= 0.7.
X2
(a) Find Lagrange interpolating polynomial for f(x) using the three given nodes
leaving all coefficients correct to 5 decimal places.
(b) Using the nodes xo and x1, construct the Hermite interpolating polynomial H3(x)
for f(x) using the Lagrange coefficient polynomials expressing all coefficients
correct to 5 decimal places.
(c) Determine the natural cubic spline that interpolates the data
f(0) = 0, f(1) = 1, ƒ(3) = 4
and find the approximate value of f(1.2) correct to four decimal places
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
