Interpolation and splines

Concepts

• Rolle's theorem from Calculus 20 exercisesIf f is continuous on [a,b], differentiable on (a,b) and f(a)=f(b), there is at least one c∈(a,b) with f^prime(c)=0.
• Newton divided differences 10 exercisesNewton divided differences are recursive quotients of function values at nodes that serve as the coefficients of the interpolatin…
• Interpolation error 10 exercisesThe interpolation error is the difference between f(x) and the polynomial P(x) that approximates it at the nodes x_0,dots,x_n; it…
• Runge phenomenon 10 exercisesThe Runge phenomenon is the oscillatory, divergent behavior of polynomial interpolation errors at high degree when the nodes are…
• Cubic splines 10 exercisesA 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…