Spectral methods are very efficient numerical algorithms for solving partial differential equations in relatively simple geometries. The numerical errors introduced by spectral algorithms typically ...

Eigenvalue problems are a cornerstone of modern applied mathematics, arising in diverse fields from quantum mechanics to structural engineering. At their heart, these problems seek scalar values and ...

In this research field we are developing advanced computational methods centered around efficient solution strategies for partial differential equations. In numerical analysis, we focus on developing ...

1 Introduction: Consequences of Numerical Inaccuracy 1 -- 1.1 Importance of Understanding Computational Statistics 1 -- 1.2 Brief History: Duhem to the Twenty-First Century 3 -- 1.3 Motivating Example ...

Root mean square error (rms, or its square, the variance distance) is often used to measure differences between simulated and observed fields. In this case ...

Due to the chaotic nature of the atmosphere, weather forecasts, even with ever improving numerical weather prediction models, eventually lose all skill. Meteorologists have a strong desire to better ...