README.md

Author: MWillettM

README.md

@@ -1,30 +1,29 @@
 This is a Python implementation of the Faul-Goodsen-Powell algorithm which produces an interpolant for d-dimensional data using the multiquadric radial basis functions. It works well for even very high dimensional data.
 
-INSTALLATION/REQUIREMENTS:
-Python > 3.11.8
+**INSTALLATION/REQUIREMENTS:**
 
-Numpy
+Python  and Numpy
 
-ALGORITHM DESCRIPTION - inputs - FGP(data, values, q, c, error)
-Data centers (x_i) and values at those points (f_i)
+**ALGORITHM DESCRIPTION** - inputs - FGP(data, values, q, c, error)
+Data centers ($x_i$) and values at those points ($f_i$)
 
 Error
 
-Two parameters for the algorithm - q and c:
+Two parameters for the algorithm - $q$ and $c$:
 
-c>0, using a smaller value (O(10^-1) or smaller) is advised. This is the 'shape parameter' for the multiquadric.
+$c>0$, using a smaller value ($O(10^{-1})$ or smaller) is advised. This is the 'shape parameter' for the multiquadric.
 
-q>0, using a value of q=30 is standard - feel free to go between 5 and 50. A rule of thumb is that smaller q means each iteration is quicker, but we may need more iterations for convergence overally. 
+$q>0$, using a value of q=30 is standard - feel free to go between 5 and 50. A rule of thumb is that smaller q means each iteration is quicker, but we may need more iterations for convergence overally. 
 
-ALGORITHM DESCRIPTION - outputs
+**ALGORITHM DESCRIPTION** - outputs
 
 Iteration count - k
 
 The interpolant, s(x) is of the form 
 
-$s(x) = sum_i^n lambda_i phi(x-x_i) + alpha$
+$s(x) = \sum_i^n \lambda_i \phi(\|x-x_i\|) + \alpha$
 
-where the x_i are the data centers and phi(x) = (x^2+c^2)^0.5 is the multiquadric radial basis function.
+where the $x_i$ are the data centers and $\phi(x) = (x^2+c^2)^{\frac{1}{2}}$ is the multiquadric radial basis function.
 
 The algorithm returns the coefficients lambda_i and the value of alpha.