Exercise · ZW-CUBIC-SPLINES-006 · ★★☆ Intermediate

A natural spline with \(n=3\) intervals has \(4\cdot3=12\) unknowns. How many interpolation and continuity equations are there in total, not counting the boundary ones?

Choose one option.

Show answer
  • C. 10

Explanation

There are \(2n\) interpolation conditions and \(2(n-1)\) continuity conditions for \(S'\) and \(S''\) at interior nodes, totaling \(10\) for \(n=3\).

Study Numerical methods in ZWMath →

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-005 ZW-CUBIC-SPLINES-007 →