Exercise · ZW-CUBIC-SPLINES-008 · ★★☆ Intermediate
A clamped spline imposes \(S'(x_0)=f'(x_0)\). Which of these statements about it is correct?
Choose one option.
Show answer
- A. It requires knowing the derivative of the function at the endpoints
Explanation
The clamped condition requires the value of \(f'\) at the endpoints, and it does not force \(S''\) to zero nor change the number of pieces.
Review the concept: Cubic splines
A cubic spline \(S\) is a piecewise function, each piece a polynomial of degree three, that interpolates the data \((x_i,y_i)\) and is of class \(C^2\) at the nodes.
\[S_i(x)=a_i+b_i(x-x_i)+c_i(x-x_i)^2+d_i(x-x_i)^3\]
More practice problems: cubic splines
- ZW-CUBIC-SPLINES-001 What degree is each piece of a cubic spline?
- ZW-CUBIC-SPLINES-002 What class of continuity does a cubic spline have at interior nodes?
- ZW-CUBIC-SPLINES-003 Which boundary condition defines the natural spline?
- ZW-CUBIC-SPLINES-004 How many cubic pieces does a spline have over n intervals?
- ZW-CUBIC-SPLINES-005 What type of linear system appears when computing the coefficients c_i?
- ZW-CUBIC-SPLINES-006 A natural spline with n=3 intervals has 4·3=12 unknowns. How many interpolation and continuity equa…
- ZW-CUBIC-SPLINES-007 For the natural spline through (0,0),(1,1),(2,0), what is S''(1) using the c_1 form of the system?
- ZW-CUBIC-SPLINES-009 If S is a natural cubic spline with S''(x_0)=0, what happens to c_0 in the piecewise representation?