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# Fast multiplication of constant symmetric positive-definite matrix and vector.

Consider the matrix $H=H^T$, $H>0$, $H \in R^{n \times n}$, and the vector $v \in R^n$. In a numerical algorithm, I need to compute the product $b = Hv$. Right now I am following the naive approach: $b_i = \sum_{j=1}^{n} h_{ij} v_j, i=1,...,n$. Is there a faster way to compute this product? $H$ is non-sparse and constant (i.e. eigenvectors, eigenvalues, etc. of $H$ are available).