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math.NA2022
Complex matrix inversion via real matrix inversions
Zhen Dai, Lek-Heng Lim, Ke Ye
We study the inversion analog of the well-known Gauss algorithm for multiplying complex matrices. A simple version is $(A + iB)^{-1} = (A + BA^{-1}B)^{-1} - i A^{-1}B(A+BA^{-1} B)^…
math.NA2022
Numerical stability and tensor nuclear norm
Zhen Dai, Lek-Heng Lim
We present a notion of bilinear stability, which is to numerical stability what bilinear complexity is to time complexity. In bilinear complexity, an algorithm for evaluating a bil…