Lagrange1

Lagrange1(num_elems: int)

Piecewise linear polynomials.

Parameters

num_elems : int

The number of elements to use.

Notes

To construct a piecewise linear basis, we divide the interval \([0, 1]\) into num_elems equisized elements. Then, within each element a given function can be represented by \[ f(x) \approx f(x_{0}) + \frac{f(x_{1}) - f(x_{0})}{x_{1} - x_{0}}(x - x_{0}), \] where \(x_{0}\) and \(x_{1}\) denote the endpoints of the element.

We use piecewise cubic polynomials to represent the (conditional) CDFs corresponding to the piecewise linear representation of (the square root of) the target density function.