In statistics, non-linear iterative partial least squares (NIPALS) is an algorithm for computing the first few components in a principal component or partial least squares analysis. For very-high-dimensional datasets, such as those generated in the 'omics sciences (e.g., genomics, metabolomics) it is usually only necessary to compute the first few principal components. The nonlinear iterative partial least squares (NIPALS) algorithm calculates t1 and p1' from X. The outer product, t1p1' can then be subtracted from X leaving the residual matrix E1. This can be then used to calculate subsequent principal components.  This results in a dramatic reduction in computational time since calculation of the covariance matrix is avoided.
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