Linear Algebra
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
Low-Variance Randomised Numerical Linear Algebra for Finite Element Simulation
arXiv:2606.08817v1 Announce Type: new Abstract: We present a low-variance randomised numerical linear algebra approach for multi-query finite element systems arising from parametric elliptic partial differential equations with applications to digital twins and online model calibration. The method relies on Galerkin subspace projection for reducing the dimensionality, and then combines parameter-oblivious leverage-score Bernoulli sampling with a control variates scheme to yield a...
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...
Lie algebraic invariants in quantum linear optics
arXiv:2409.12223v3 Announce Type: replace-cross Abstract: Quantum linear optics without post-selection is not powerful enough to produce any quantum state from a given input state. This limits its utility since some applications require entangled resources that are difficult to prepare.
Application of polynomial algebras to non-linear equation solvers
Announce Type: new Abstract: This paper presents a novel application of Jet Transport, a high-order automatic differentiation technique, to enhance classical numerical methods, with a focus on Newton's method. We prove a central theorem establishing that, under appropriate conditions, applying Jet Transport within a Newton iteration doubles the number of correct coefficients in the Taylor series approximation of the solution. This theoretical result is then extended to the practical case...
Explicit and asymptotically good constructions of Algebraic Geometry codes in the sum-rank metric
Announce Type: new Abstract: Algebraic Geometry (AG) codes (i.e. linear codes from algebraic function fields) in the Hamming metric were proposed by Goppa in 1980 and have been intensively studied ever since. Linearized Algebraic Geometry codes, the analogue of AG codes in the sum-rank metric, were instead introduced more recently [9], using quotients of the ring of Ore polynomials with coefficients in an algebraic function field.
Solving 2D Black Scholes Equation via Hermitian Block Embedding and Generalised Quantum Signal Processing
arXiv:2606.00458v1 Announce Type: cross Abstract: The Black Scholes equation provides a fundamental model for the no arbitrage pricing of financial derivatives. After finite difference discretisation, the pricing problem can be formulated as a finite dimensional linear algebra problem involving the inverse of a non Hermitian time step matrix. Recent advances in quantum linear algebra algorithms, particularly the generalised quantum signal processing (GQSP)algorithm, enable matrix functions...
Tomography by Design: An Algebraic Approach to Low-Rank Quantum States
arXiv:2602.15202v2 Announce Type: replace-cross Abstract: We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be obtained solely using standard numerical linear algebra operations. The proposed algebraic matrix completion framework applies to a broad class of generic, low-rank mixed quantum states and, compared...
Pauli-structured preconditioning for quantum linear system solvers
arXiv:2606.01733v1 Announce Type: cross Abstract: Preconditioning is a fundamental technique for accelerating classical linear system solvers, and understanding when its benefits persist in quantum linear system (QLS) solvers is important for assessing the practical resource requirements of quantum linear algebra. In QLS algorithms, however, the potential advantage of preconditioning may be offset by the normalization overhead incurred by composing separate block-encodings of the system...
TorchKM: A GPU-Oriented Library for Kernel Learning and Model Selection
Announce Type: new Abstract: TorchKM is an open-source library for kernel machines, including support vector machines, kernel logistic regression, and kernel quantile regression, with GPU acceleration. The library features a scikit-learn-style API and is designed to exploit GPU-friendly linear algebra, accelerating the full training and model-selection pipeline through intelligent reuse of matrix operations. Benchmarks show competitive predictive performance together with substantial...
A Unified Heterogeneous Implementation of Numerical Atomic Orbitals-Based Real-Time TDDFT within the ABACUS Package
Announce Type: replace-cross Abstract: We present a unified heterogeneous computing framework for real-time time-dependent density functional theory (RT-TDDFT) based on numerical atomic orbitals (NAOs), implemented in the ABACUS package. We introduce three co-designed abstraction layers, including unified data containers, unified linear algebra operators, and unified grid integration interfaces. These layers collectively accelerate the two most demanding parts of NAO-based RT-TDDFT: explicit...