A fast algorithm for the recursive calculation of dominant singular subspaces
Journal of Computational and Applied Mathematics
A Fast Algorithm for Updating and Downsizing the Dominant Kernel Principal Components
SIAM Journal on Matrix Analysis and Applications
Journal of Computational and Applied Mathematics
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In this paper we show how to compute recursively an approximation of the left and right dominant singular subspaces of a given matrix. In order to perform as few as possible operations on each column of the matrix, we use a variant of the classical Gram-Schmidt algorithm to estimate this subspace. The method is shown to be particularly suited for matrices with many more rows than columns. Bounds for the accuracy of the computed subspace are provided. Moreover, the analysis of error propagation in this algorithm provides new insights in the loss of orthogonality typically observed in the classical Gram-Schmidt method.