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 ...

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 ...