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math.NA2026
Advanced Linear Algebra with Applications - Part I (Numerical linear algebra for PDEs, machine learning, and data assimilation)
Victorita Dolean, Jemima Tabeart
These lecture notes form the first part of a master's-level course on advanced numerical linear algebra. Their aim is not only to present the classical algorithms, but to show why…
math.NA2025
An Introduction to Solving the Least-Squares Problem in Variational Data Assimilation
I. Daužickaitė, M. A. Freitag, S. Gürol +4
Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weath…
math.NA2025
Block Alpha-Circulant Preconditioners for All-at-Once Diffusion-Based Covariance Operators
Jemima M. Tabeart, Selime Gürol, John W. Pearson +1
Covariance matrices are central to data assimilation and inverse methods derived from statistical estimation theory. Previous work has considered the application of an all-at-once…