Linear Interpolation for Given Function

  • Context: Undergrad 
  • Thread starter Thread starter ForTheGreater
  • Start date Start date
  • Tags Tags
    Linear
Click For Summary
SUMMARY

The discussion centers on determining the linear interpolant for the function defined by specific values at points: f(-π)=4, f(-π/2)=5/4, f(0)=1, f(π/2)=-3/4, and f(π)=0. The correct approach involves using linear interpolation formulas, specifically the equation of the straight line connecting points (-π, 4) and (-π/2, 5/4). The first interpolant for the interval from -π to -π/2 is given as 4 - 11(x + π)/(2π). The user expresses confusion regarding the problem's requirements, questioning whether they need to provide all interpolants or just the connecting equations.

PREREQUISITES
  • Understanding of linear interpolation techniques
  • Familiarity with Lagrange basis functions
  • Knowledge of trigonometric functions and their properties
  • Basic calculus concepts, particularly derivatives and limits
NEXT STEPS
  • Study linear interpolation methods in detail
  • Learn about Lagrange interpolation and its applications
  • Explore the properties of trigonometric functions in interpolation
  • Practice deriving linear equations from given points
USEFUL FOR

Students and professionals in mathematics, particularly those focused on numerical methods, data interpolation, and calculus. This discussion is beneficial for anyone looking to enhance their understanding of linear interpolation techniques.

ForTheGreater
Messages
22
Reaction score
0
Decide the linear interpolant

f(-pi)=4 f(-pi/2)=5/4 f(0)=1 f(pi/2)=-3/4 f(pi)=0

the function is (1/pi2 ) (x-pi)2 - cos2 (x-pi/2)

Don't know how to do this. I tried lagrange basis functions f(x0)(x1-x)/(x1-x0)+f(x1)(x-x0)/(x1-x0)

But it doesn't turn out right.

The answer for the first interpolant (interval -pi to -pi/2) is: 4-11(x+pi)/(2pi)
 
Mathematics news on Phys.org
I sense a contradiction between the problem statement "Decide the interpolant" and the book answer "The answer for the first interpolant ... is...".
Could it be that all you are asked to provide is the four equations "connecting the dots" ?

(The book answer for the first section is the equation of the straight line through ##(-\pi, 4)## and ##(-\pi/2, 5/4)##. )

--
 
I have the answer here, it wasn't in the problem.

I'm suppose to give the interpolant in all intervals, or as you put it connect the dots.

Thank you!
 

Similar threads

MHB Interpolating Points with Continuous Modular Functions?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Comparing ##a^b## and ##b^a##
  • · Replies 19 ·
Replies
19
Views
2K
Undergrad Alternating Harmonic Numbers are cool, spread the word!
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Taylor expansion of an unknown function
  • · Replies 5 ·
Replies
5
Views
3K
Amplitude of harmonic oscillation given position and velocity
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Transformation of Functions: How Do Domain and Range Change?
  • · Replies 4 ·
Replies
4
Views
2K
Python Finding a local max/min of a function in Python
  • · Replies 7 ·
Replies
7
Views
5K
Undergrad Why is it important to convert angle units when using trigonometric functions?
  • · Replies 8 ·
Replies
8
Views
2K
MHB What are the domain and range for the inverse function $f^{-1}$ of $f$?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Recursive square root inside square root problem
  • · Replies 27 ·
Replies
27
Views
6K