Suppose that the problem is to linearize a curve through three-dimensional space. These three variables define a curve in three-dimensional space. These data are completely described by three linear components, but they define a single curve, which could be described as a single nonlinear component.
Splines are curves, which are usually required to be continuous and smooth.
Splines are usually defined as piecewise polynomials of degree n with function values and first n -1 derivatives that agree at the points where they join. The abscissa values of the join points are called knots . Splines with no knots are generally smoother than splines with knots, which are generally smoother than splines with multiple discontinuous derivatives. Knots give the curve freedom to bend to more closely follow the data. The algorithm did not converge with 50 iterations, so more iterations may be needed for this problem.