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LAPACK has an implementation of the svd of a 2x2 triangular matrix. It appears to be very robust. The routine is XLASV2. To apply to a regular 2x2 matrix, you can simply apply a single givens rotation from the left/right.


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I'm no expert on software and certainly not on GPU software, but I can hopefully give some advice of a mathematical nature that might be helpful to you. Given a matrix $W$, one can embed $W$ in the larger square and Hermitian matrix $$ B = \begin{bmatrix} 0 & W \\ W^* & 0 \end{bmatrix}. $$ $B$ is a square matrix with twice the number of nonzeros as $...


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