Sign-embedding quantum algorithms deliver explicit block-encodings for Sylvester equations and related matrix problems with query complexity linear in inverse-conditioning parameters and logarithmic in error tolerance.
Byers,Solving the algebraic Riccati equation with the matrix sign function, Linear Algebra and its Applications85(1987), 267–279
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Sign Embedding Quantum Algorithms for Matrix Equations and Matrix Functions
Sign-embedding quantum algorithms deliver explicit block-encodings for Sylvester equations and related matrix problems with query complexity linear in inverse-conditioning parameters and logarithmic in error tolerance.