What is a Spline Function -How do I choose the order m of a spline?
We need to know what the essential characteristics of splines are before we consider how to construct a basis system for them. Spline functions are formed by joining polynomials together at fixed points called knots. That is, we divide the interval extending from lower limit tL to upper limit tU over which we wish to approximate a curve into L+1 sub-intervals separated by L interior boundaries ξl called knots, or sometimes breakpoints.) There is a distinction between these two terms, but we will come to this later. Consider the simplest case in which a single breakpoint divides interval [tL; tU] into two subintervals. The spline function is, within each interval, a polynomial of specified degree (the highest power defining the polynomial) or order (the number of coefficients defining the polynomial, which is one more than its degree). Let’s use m to designate the order of the polynomial, so that the degree is m – 1: At the interior breakpoint ξ1, the two polynomials are required to joi
