Pseudospectral Approximation of Functions

April 6, 2018   •   Joshua Lytle
My graduate research at BYU relied on good boundary value problem (BVP) solvers. So I had the chance to review a lot of what was already implemented in Python, and build several of my own implementations. One approach that I've really enjoyed learning about is the pseudospectral method. This blog post will focus on approximating functions with Chebychev polynomials. I plan to eventually discuss a pseudospectral BVP solver.

Evaluation Metrics for Regression Models

April 6, 2018   •   Joshua Lytle
So I recently wanted to clarify my thinking about two commonly used error metrics for evaluating regression models - mean absolute error (MAE) and root mean squared error (RMSE). These metrics accomplish similar tasks, but each have their own advantages. Let $\mathcal{E} = (e_1,\ldots,e_n)^T$ be the model errors over the test data $(x_i,y_i)$. MAE is a straightforward mean of the absolute value of the errors, $\frac{1}{n}\sum_{i=1}^n |e_i|$. RMSE is the square root of the mean of the squared errors, $\sqrt{ \frac{1}{n}\sum_{i=1}^n e_i^2 \,}$.