Performance and Accuracy of xPTEQR

xPTEQR is a LAPACK function for the computation of the  eigendecomposition of a symmetric positive definite tridiagonal matrix. I compare the performance and accuracy of xPTEQR to the other symmetric eigensolvers in LAPACK 3.5.0.

In layman’s terms, there are several algorithms available on a computer that calculate the eigenvectors and eigenvalues of matrices with special properties (symmetric, positive definite, tridiagonal). xPTEQR is the name of the computer implementation of one of those algorithms and I am not aware of any measurements with it. In this blog post I compare xPTEQR in terms of speed and accuracy to other good algorithms. In the figures below, xPTEQR can be found under the label "SVD" (xPTEQR is the name of the implementation, SVD is the algorithm). Moreover, in every figure it holds that lower is better.

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