# What is a polyharmonic spline?

## What is a polyharmonic spline?

A polyharmonic spline is a linear combination of polyharmonic radial basis functions (RBFs) denoted by ϕ {\\displaystyle \\phi } plus a polynomial term:

## What is the Newton-Raphson method in MATLAB?

Newton-Raphson Method MATLAB Program. Newton-Raphson method, named after Isaac Newton and Joseph Raphson, is a popular iterative method to find the root of a polynomial equation. It is also known as Newton’s method, and is considered as limiting case of secant method.

**What is a polyharmonic equation?**

A polyharmonic equation is a partial differential equation of the form Δ m f = 0 {\\displaystyle \\Delta ^{m}f=0} for any natural number m {\\displaystyle m} .

**What is the iteration formula for Newton Raphson in MATLAB?**

Using Newton’s iteration formula: x 2 = x 1 – f(x 1)/f’(x 1) = 1.5 – 0.875/5.750 = 1.34782600. The iteration for x 3, x 4, …. is done similarly. The table below shows the whole iteration procedure for the given function in the program code for Newton Raphson in MATLAB and this numerical example.