Krylov
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Related Articles from SNS
Optimal Stochastic Krylov based Techniques for Large- Scale Log-Determinant Estimation
arXiv:2606.07004v1 Announce Type: new Abstract: Estimating the logarithm of the determinant of large sparse positive definite symmetric matrices is an important task in numerical linear algebra, machine learning, Gaussian processes, and uncertainty quantification. In this work, we introduce two scalable and efficient methods for large-scale log-determinant termed the Optimal Stochastic Arnoldi with Incomplete Orthogonalization Procedure (OSA-IOP) and the Optimal Stochastic Lanczos Quadrature...
Causal Unlearning in Collaborative Optimization: Exact and Approximate Influence Reversal under Adversarial Contributions
arXiv:2605.20341v2 Announce Type: replace Abstract: Federated learning systems must support data deletion requests to comply with privacy regulations, yet retraining from scratch after each deletion is computationally prohibitive. We present HF-KCU, a method that removes a client's contribution by approximating the influence function through conjugate gradient iterations in Krylov subspaces, reducing complexity from O(d^3) to O(kd) where k<<d. A causal weighting mechanism ensures that only...
JAX-AMG: A GPU-Accelerated Differentiable Sparse Linear Solver Library for JAX
Announce Type: new Abstract: Sparse linear systems from PDE discretizations are central to scientific computing, yet no existing JAX-ecosystem solver simultaneously provides GPU-accelerated algebraic multigrid (AMG), automatic differentiation (AD), and distributed multi-GPU execution. JAX-AMG fills this gap by wrapping the Nvidia AmgX solver suite as a native JAX primitive, exposing AMG and Krylov methods with configurable preconditioners through a unified interface compatible with JIT...
JAX-AMG: A GPU-Accelerated Differentiable Sparse Linear Solver Library for JAX
Announce Type: cross Abstract: Sparse linear systems from PDE discretizations are central to scientific computing, yet no existing JAX-ecosystem solver simultaneously provides GPU-accelerated algebraic multigrid (AMG), automatic differentiation (AD), and distributed multi-GPU execution. JAX-AMG fills this gap by wrapping the Nvidia AmgX solver suite as a native JAX primitive, exposing AMG and Krylov methods with configurable preconditioners through a unified interface compatible with JIT...
A fast reduced order method for linear parabolic inverse source problems
arXiv:2306.05677v2 Announce Type: replace Abstract: In this paper, we propose a novel, computationally efficient reduced order method to solve linear parabolic inverse source problems. Our approach provides accurate numerical solutions without relying on specific training data. The forward solution is constructed using a Krylov sequence, while the source term is recovered via the conjugate gradient (CG) method.
A Low-rank Interpolatory Projection Algorithm for Solving Large-scale T-Sylvester Equations
arXiv:2606.05640v1 Announce Type: new Abstract: This paper considers large-scale T-Sylvester equations of the form $AX - X^\top E^\top + B_1B_2^\top = 0$, which admit a low-rank solution. It is shown that when the unique solution of the T-Sylvester equation is low-rank, the problem naturally reduces to a tangential interpolation problem via oblique projection. The specific interpolation points and tangential directions needed to obtain the low-rank solution are not known a priori, thus...
A Tensor Network Framework for Lindbladian Spectra and Steady States
Announce Type: replace-cross Abstract: Quantum systems coupled to (non-)Markovian environments attract increasing attention due to their peculiar physical properties. Exciting prospects such as unconventional non-equilibrium phases beyond the Mermin-Wagner limit or dissipative state preparation demand a systematic analysis of quantum many-body phases out of equilibrium.
A Perturbed q-Tsallis Self-Concordant Barrier for Spectrally Robust Semidefinite Programming
Announce Type: cross Abstract: We introduce and analyse a perturbed $q$-Tsallis barrier for semidefinite programming (SDP), defined as a spectral perturbation of the classical log-det barrier on the cone of positive definite matrices. The barrier introduces eigenvalue-adaptive stiffening through a Tsallis-type matrix-power term controlled by parameters $q>1$ and $\eta\geq0$. Our main theoretical contribution is a sharp characterisation of the differential self-concordance regime of the...
An Efficient Parity-Blocked Method for Band-Structure Computation of 3D Anisotropic Phononic Crystals
new Abstract: Band-structure calculations for three-dimensional anisotropic phononic crystals require the repeated solution of large elastic generalized eigenvalue problems along Bloch paths. In standard staggered-grid discretizations, anisotropic coupling may involve derivative components located at incompatible grid positions, so additional interpolation or averaging closures are often introduced. This paper proposes a parity-blocked rotated staggered discretization based on four...
Transpose-free linear algebra
arXiv:2606.01335v1 Announce Type: new Abstract: We study the limitations of matrix-free algorithms that access a matrix $A$ only through forward matrix-vector products (matvecs) $x \mapsto Ax$, without access to the transpose $A^\top$ or its action. This setting arises naturally in operator learning, inverse problems, and matrix-free PDE solvers, where adjoint evaluations may be unavailable or prohibitively expensive. We show that the lack of transpose access creates severe and sometimes...