Natural splines

Expanding the equations we get

Interpolation condition:

Continuity of the 1st derivative:

Continuity of the 2nd derivative:

For all internal points i we have 4 equations; total

of 4(N-1), for N points. We add 2 interpolating conditions on endpoints, and 2 requirements that 2nd derivatives are 0 at endpoints. We get a complete linear system with 4N unknowns

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