The symmetric matrix *A* could be represented as *A=Q·T·Q ^{ T}*, where

Like other algorithms of orthogonal factorization (for example, QR and LQ decomposition algorithms), this algorithm uses a sequence of elementary reflections to transform the matrix *A*. The transformations are applied to the matrix both from the right and from the left, preserving the matrix symmetry on each stage and sequentially removing non-diagonal elements.

As a result of **SMatrixTD** subroutine, matrix *A* is replaced by the tridiagonal matrix *T* and a sequence of reflections transformations stored in a compact form. The format of the matrix and the subroutine parameters are described in detail in the subroutine comments; there we can note an analogy with QR-decomposition, that uses the lower triangular part of the matrix *R* to store the matrix *Q* and utilizes a very similar data storage format. As with QR decomposition, a subroutine for "unpacking" the matrix *Q* is presented: **SMatrixTDUnpackQ**.

*This algorithm is transferred from the LAPACK library.*

*This article is licensed for personal use only.*

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