### Dlasq2 input format

Posted:

**Thu Nov 12, 2015 2:40 pm**I'm trying to understand the input format for Dlasq2 (http://www.netlib.org/lapack/explore-ht ... q2_8f.html). The documentation states

DLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd array Z to high relative accuracy are computed to high relative accuracy, in the absence of denormalization, underflow and overflow. To see the relation of Z to the tridiagonal matrix, let L be a unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and let U be an upper bidiagonal matrix with 1's above and diagonal Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the symmetric tridiagonal to which it is similar.

I don't understand this as the L and U matrices described do not multiply to a symmetric tridiagonal matrix ( if L = [1, 0; a, 0] and U = [b, 1; 0, c]. L*U = [b, 1; ab, a+c]). How do I find the "symmetric tridiagonal to which it is similar"?

DLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd array Z to high relative accuracy are computed to high relative accuracy, in the absence of denormalization, underflow and overflow. To see the relation of Z to the tridiagonal matrix, let L be a unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and let U be an upper bidiagonal matrix with 1's above and diagonal Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the symmetric tridiagonal to which it is similar.

I don't understand this as the L and U matrices described do not multiply to a symmetric tridiagonal matrix ( if L = [1, 0; a, 0] and U = [b, 1; 0, c]. L*U = [b, 1; ab, a+c]). How do I find the "symmetric tridiagonal to which it is similar"?