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# Multiscale Eigenbasis Calculations : N Eigenfunctions in O ( N log N )

@inproceedings{LivneMultiscaleEC, title={Multiscale Eigenbasis Calculations : N Eigenfunctions in O ( N log N )}, author={O. E. Livne and Achi Brandt} }

Motivated by quantum chemical calculations, we explore a novel multiscale approach for computing, storing, and expanding in many eigenfunctions of differential operators. This approach leads to efficient multiscale eigenbasis algorithms, which typically scale as O(N logN), where N is the number of eigenfunctions. In particular, they provide a vast generalization of the Fast Fourier Transform (FFT) algorithm, which expands in Fourier series, to expansions in terms of eigenfunctions of a general… CONTINUE READING