Arrowhead Factorization and its Applications in Optimized Eigendecomposition

What is it about?

Eigendecomposition is a fundamental mathematical operation used in many scientific and engineering applications, and it is essential to develop optimised algorithms that allow us to solve new and increasingly complex problems. In this work we introduce a novel matrix factorisation used for efficient eigendecomposition of a certain matrices in the class of generalised arrowhead matrices and showcase its practical applications by solving a quantum tunnelling problem.

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Photo by Dan Cristian Pădureț on Unsplash

Photo by Dan Cristian Pădureț on Unsplash

Why is it important?

Full eigendecomposition of a matrix is an expensive operation that can often cause bottlenecks in modern scientific and engineering software. By developing optimised algorithms, we are able to reduce the time-to-solution, saving both money and resources. Moreover, we unlock the possibility of exploring larger and more complex systems that would otherwise have prohibitive costs.