A deflation-based preconditioner is proposed to robustly handle ill-conditioned systems arising from small cut elements in immersed finite element methods.
Saad, Iterative methods for sparse linear systems, SIAM
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qANM applies high-order perturbation via Taylor series to convert nonlinear systems to linear equations solved by variational quantum linear solver and quantum Jacobi method, with simulator validation and 98% accuracy on a noisy superconducting processor.
Introduces an optimized error reallocation for stochastic Lanczos quadrature that minimizes total matrix-vector multiplications by allocating more budget to the Lanczos process than to Monte Carlo sampling for a target accuracy.
DFPI is a unified framework for deflated fixed-point iterations that organizes RPM, Anderson acceleration, BoostConv and Krylov methods like GMRES under projection operators and trouble-vector recruitment, with a convergence result tied to projection-space invariance.
citing papers explorer
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Deflation-based preconditioning for immersed finite element methods and immersogeometric analysis
A deflation-based preconditioner is proposed to robustly handle ill-conditioned systems arising from small cut elements in immersed finite element methods.
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A quantum nonlinear solver based on the asymptotic numerical method
qANM applies high-order perturbation via Taylor series to convert nonlinear systems to linear equations solved by variational quantum linear solver and quantum Jacobi method, with simulator validation and 98% accuracy on a noisy superconducting processor.
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An analysis on stochastic Lanczos quadrature with asymmetric quadrature nodes
Introduces an optimized error reallocation for stochastic Lanczos quadrature that minimizes total matrix-vector multiplications by allocating more budget to the Lanczos process than to Monte Carlo sampling for a target accuracy.
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DFPI, A unified framework for deflated linear solvers: bridging the gap between Krylov subspace methods and Fixed-Point Iterations
DFPI is a unified framework for deflated fixed-point iterations that organizes RPM, Anderson acceleration, BoostConv and Krylov methods like GMRES under projection operators and trouble-vector recruitment, with a convergence result tied to projection-space invariance.