Results 61 to 70 of about 12,661,880 (175)

A Method of Indefinite Krylov Subspace for Eigenvalue Problem [PDF]

Mathematical Problems in Engineering, 2018
We describe an indefinite state of Arnoldi’s method for solving the eigenvalues problems. In the following, we scrutinize the indefinite state of Lanczos’ method for solving the eigenvalue problems and we show that this method for the J-Hermitian matrices works much better than Arnoldi’s method.
M. Aliyari, M. Ghasemi Kamalvand
openaire   +1 more source

Compile‐Once Block Encodings for Masked Similarity‐Transformed Effective Hamiltonians

Advanced Quantum Technologies, Volume 9, Issue 9, September 2026.
Composer transforms structured electronic‐structure operators into a reusable quantum‐circuit fabric. Once compiled, the same block‐encoding architecture is re‐dialed through coefficients, rotation angles, and masks to generate similarity‐transformed effective Hamiltonians across related problem instances, avoiding repeated structural recompilation ...
Bo Peng, Yuan Liu, Karol Kowalski
wiley   +1 more source

An Alternative HSS Preconditioner for the Unsteady Incompressible Navier-Stokes Equations in Rotation Form

Journal of Applied Mathematics, 2012
We study the preconditioned iterative method for the unsteady Navier-Stokes equations. The rotation form of the Oseen system is considered. We apply an efficient preconditioner which is derived from the Hermitian/Skew-Hermitian preconditioner to the ...
Jia Liu
doaj   +1 more source

Detecting When One Probe Vector is Enough for Preconditioned Log‐Determinant Approximation

Numerical Linear Algebra with Applications, Volume 33, Issue 4, August 2026.
ABSTRACT We present randomized algorithms for estimating the log‐determinant of regularized symmetric positive semi‐definite matrices. The algorithms access the matrix only through matrix vector products, and are based on the introduction of a preconditioner and stochastic trace estimator.
Alice Cortinovis, Daniele Toni
wiley   +1 more source

Krylov Implicit Integration Factor Methods for Semilinear Fourth-Order Equations

Mathematics, 2017
Implicit integration factor (IIF) methods were developed for solving time-dependent stiff partial differential equations (PDEs) in literature. In [Jiang and Zhang, Journal of Computational Physics, 253 (2013) 368–388], IIF methods are designed to ...
Michael Machen, Yong-Tao Zhang
doaj   +1 more source

Spectral Analysis of Block Diagonally Preconditioned Multiple Saddle‐Point Matrices With Inexact Schur Complements

Numerical Linear Algebra with Applications, Volume 33, Issue 4, August 2026.
ABSTRACT We derive eigenvalue bounds for symmetric block‐tridiagonal multiple saddle‐point systems preconditioned with block‐diagonal Schur complement matrices. This analysis applies to an arbitrary number of blocks and accounts for the case where the Schur complements are approximated, generalizing the findings in [11, Bergamaschi et al., Linear ...
Marco Pilotto, Luca Bergamaschi, Ángeles Martínez   +2 more
wiley   +1 more source

A Time-Segmented SAI-Krylov Subspace Approach for Large-Scale Transient Electromagnetic Forward Modeling

Applied Sciences
After nearly two decades of development, transient electromagnetic (TEM) 3D forward modeling technology has significantly improved both numerical precision and computational efficiency, primarily through advancements in mesh generation and the ...
Ya’nan Fan, Kailiang Lu, Juanjuan Li, Tianchi Fu   +3 more
doaj   +1 more source

A note on augmented unprojected Krylov subspace methods

ETNA - Electronic Transactions on Numerical Analysis, 2022
14 pages, 4 ...
openaire   +4 more sources

The Use of Restarted Krylov Methods for Large Sparse Least Squares Problems

Numerical Linear Algebra with Applications, Volume 33, Issue 4, August 2026.
ABSTRACT The use of restarted Krylov methods for solving large sparse linear least squares problems suffers from certain inherited difficulties. One of them arises in ill‐conditioned problems, when part of the residual vector is spanned by singular vectors that correspond to small singular values.
Achiya Dax
wiley   +1 more source

Mixed Precision Augmented GMRES

Numerical Linear Algebra with Applications, Volume 33, Issue 4, August 2026.
ABSTRACT We aim to accelerate the restarted generalized minimal residual (GMRES) method for the solutions of linear systems by combining two types of techniques. On the one hand, mixed precision GMRES algorithms, which use lower precision in certain steps of the inner cycles, offer significant reductions in computational and memory costs.
Yongseok Jang, Pierre Jolivet, Théo Mary   +2 more
wiley   +1 more source