Related papers: Block cross-interactive residual smoothing for Lan…
Global and block Krylov subspace methods are efficient iterative solvers for large sparse linear systems with multiple right-hand sides. However, global or block Lanczos-type solvers often exhibit large oscillations in the residual norms…
We develop a block minimum residual (MINRES) algorithm for symmetric indefinite matrices. This version is built upon the band Lanczos method that generates one basis vector of the block Krylov subspace per iteration rather than a whole…
Reconfigurable intelligent surfaces (RISs) allow controlling the propagation environment in wireless networks by tuning multiple reflecting elements. RISs have been traditionally realized through single connected architectures,…
The residual cutting (RC) method has been proposed as an outer-inner loop iteration for efficiently solving large and sparse linear systems of equations arising in solving numerically problems of elliptic partial differential equations.…
We introduce an iterative method named BiLQ for solving general square linear systems Ax = b based on the Lanczos biorthogonalization process defined by least-norm subproblems, and that is a natural companion to BiCG and QMR. Whereas the…
The Lanczos algorithm has proven itself to be a valuable matrix eigensolver for problems with large dimensions, up to hundreds of millions or even tens of billions. The computational cost of using any Lanczos algorithm is dominated by the…
Within the context of massive machine-type communications+, reconfigurable intelligent surfaces (RISs) represent a promising technology to boost system performance in scenarios with poor channel conditions. Considering single-antenna…
We consider the task of computing solutions of linear systems that only differ by a shift with the identity matrix as well as linear systems with several different right hand sides. In the past Krylov subspace methods have been developed…
This work investigates a practical reconfigurable intelligent surface (RIS)-aided integrated sensing and communication (ISAC) system, where a subset of RIS elements fail to function properly and reflect incident signals randomly towards…
Bi-conjugate gradient (Bi-CG) and bi-conjugate residual (Bi-CR) methods are underlying iterative solvers for linear systems with nonsymmetric matrices. Residual smoothing is a standard technique for obtaining smooth convergence behavior of…
LSQR, a Lanczos bidiagonalization based Krylov subspace iterative method, and its mathematically equivalent CGLS applied to normal equations system, are commonly used for large-scale discrete ill-posed problems. It is well known that LSQR…
The current literature on intelligent reflecting surface (IRS) focuses on optimizing the IRS phase shifts to yield coherent beamforming gains, under the assumption of perfect channel state information (CSI) of individual IRS-assisted links,…
Science and engineering problems frequently require solving a sequence of dual linear systems. Besides having to store only few Lanczos vectors, using the BiConjugate Gradient method (BiCG) to solve dual linear systems has advantages for…
An innovative evolutionary method for the dynamic control of reconfigurable intelligent surfaces (RISs) is proposed. It leverages, on the one hand, on the exploration capabilities of evolutionary strategies and their effectiveness in…
Reconfigurable intelligent surfaces (RISs) hold significant promise for enhancing physical layer security (PLS). However, conventional RISs are typically modeled using diagonal scattering matrices, capturing only independent reflections…
We introduce an iterative solver named MINARES for symmetric linear systems $Ax \approx b$, where $A$ is possibly singular. MINARES is based on the symmetric Lanczos process, like MINRES and MINRES-QLP, but it minimizes $\|Ar_k\|$ in each…
There exist two major problems in application of the conventional block BiCGSTAB method to the O(a)-improved Wilson-Dirac equation with multiple right-hand-sides: One is the deviation between the true and the recursive residuals. The other…
The passive reconfigurable intelligent surface (RIS) requires numerous elements to achieve adequate array gain, which linearly increases power consumption (PC) with the number of reflection phases. To address this, this letter introduces a…
For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by a white noise, Lanczos bidiagonalization based LSQR and its mathematically equivalent CGLS are most commonly used. They have intrinsic…
For solving large consistent linear systems by iteration methods, inspired by the maximum residual Kaczmarz method and the randomized block Kaczmarz method, we propose the maximum residual block Kaczmarz method, which is designed to…