On the Singular Value Decomposition and Ranking Techniques

Let A be a positive non-singular n×n matrix. An approximation for a positive eigenvector for A∗A corresponding to the dominant singular value of A was suggested as the normalized version of a weighted sum of the rows of A with weights being the euclidean norms of the rows of A. In our paper we give a justification for this approach via the iteration of the power method and we show numerically that choosing the l1 norm yields better results. Applications of our results are given to ranking techniques.

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Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).