We consider a fast, data-sparse directional method to realize matrix-vector products related to point evaluations of the Helmholtz kernel. The method is based on a hierarchical partitioning of the point sets and the matrix. The considered directional multi-level approximation of the Helmholtz kernel can be applied even on high-frequency levels efficiently. We provide a detailed analysis of the almost linear asymptotic complexity of the presented method. Our numerical experiments are in good agreement with the provided theory.
CITATION STYLE
Of, G., & Watschinger, R. (2021). Complexity Analysis of a Fast Directional Matrix-Vector Multiplication. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12456 LNCS, pp. 39–59). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-67077-1_3
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