Proves relative-gap-preserving error bounds for singular vectors and eigenvectors from mixed-precision Jacobi methods that depend on the preconditioned matrix scaled condition number rather than the original.
Bini and Bruno Iannazzo and Beatrice Meini , title =
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Quantum algorithm block-encodes Riccati solutions for m-particle m-hole RPA using Riesz projectors and QSVT, claiming linear system-size scaling under sparsity and polynomial cost in excitation rank m.
Two generalizations of reduced rank extrapolation are derived for low-rank matrix sequences and iteration-dependent mapping functions, with numerical tests on Lyapunov and Riccati equations.
citing papers explorer
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Computing accurate singular vectors and eigenvectors using mixed-precision Jacobi algorithms
Proves relative-gap-preserving error bounds for singular vectors and eigenvectors from mixed-precision Jacobi methods that depend on the preconditioned matrix scaled condition number rather than the original.
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Quantum Solvers for Nonlinear Matrix Equations in Quantum Chemistry
Quantum algorithm block-encodes Riccati solutions for m-particle m-hole RPA using Riesz projectors and QSVT, claiming linear system-size scaling under sparsity and polynomial cost in excitation rank m.
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Generalizing Reduced Rank Extrapolation to Low-Rank Matrix Sequences
Two generalizations of reduced rank extrapolation are derived for low-rank matrix sequences and iteration-dependent mapping functions, with numerical tests on Lyapunov and Riccati equations.