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A low-complexity lanczos-algorithm-based detector with soft-output for multiuser massive MIMO systems

Digital Signal Processing 2017年 69卷 41-49页

作者： Xiaorong Jing Ao Li Hongqing Liu Chongqing Key Lab of Mobile Communication Technology Chongqing University of Posts and Telecommunications Chongqing China School of Communication and Information Engineering Chongqing University of Posts and Telecommunications Chongqing China

Zero-Forcing (ZF) algorithm achieves the near-optimal detection performance for massive multiple-input multiple-output (MIMO) systems at expense of performing the complicated matrix inversion of a high dimensional matrix. In this paper, a novel lanczos-algorithm-based signal detection method with soft-output is proposed to iteratively realize ZF algorithm for multiuser massive MIIMO systems, which avoids the exact computation of matrix inversion and in turn reduces the computational complexity from O ( K 3 ) to O ( K 2 ) , where K denotes the number of users. In the development of the proposed method, by analyzing the iterative process of lanczos algorithm, an approximate low-complexity scheme is proposed to calculate the log likelihood ratios (LLRs) for soft channel decoding. Simulation results show that the proposed detector provides a relatively good tradeoff between the complexity and performance compared with the several recently proposed detectors, and achieves almost the same performance as the ZF algorithm with only 3 iterations.

关键词： Massive multiple-input multiple-output (MIMO) lanczos algorithm Soft-output Signal detection Zero-forcing (ZF)

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A Node-Based Smoothed Finite Element Method (NS-FEM) for Free and Forced Vibration Analysis of Three-Dimensional (3D) Structures

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INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS 2025年第4期22卷

作者： Zhao, Jingui Liu, Guirong Huo, Shuhao Wang, Gang Sun, Chao Li, Zirui Hebei Univ Technol Sch Mech Engn Tianjin 300401 Peoples R China Hebei Univ Technol State Key Lab Reliabil & Intelligence Elect Equipm Tianjin 300130 Peoples R China Univ Cincinnati Dept Aerosp Engn & Engn Mech Cincinnati OH 45221 USA Taiyuan Univ Technol Coll Aeronaut & Astronaut Taiyuan 550001 Peoples R China

The smoothed finite element method (S-FEM) has been found to be an effective solution method for solid mechanics problems. This paper proposes an effective approach to compute the lower bound solution of free vibration and the upper bound solution of the forced vibration of solid structures, by making use of the important softening effects of the node-based smoothed finite element method (NS-FEM). Through the gradient smoothing technique, the strain-displacement matrix is obtained in the smoothing domain based on the element mesh nodes. Subsequently, the stiffness matrix is computed in a manner consistent with the standard finite element method (FEM). Here, the practical lanczos algorithm and the modal superposition technique are employed to obtain the frequencies, modes, and transient responses of a given homogeneous structure. For three-dimensional (3D) solid structures, the automatically generated four-node tetrahedron (T4) element meshes are utilized. The results obtained from the NS-FEM are compared with the standard FEM in terms of accuracy, convergence and computational efficiency.

关键词： Node-based smoothed finite element method free vibration forced vibration lanczos algorithm mode superposition method

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Rethinking eigenpairs: Community detection with orthogonality

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KNOWLEDGE-BASED SYSTEMS 2025年 311卷

作者： Yan, Liping Cao, Jie Yu, Weiren Wang, Yuyao Vukovic, Darko B. Nanjing Univ Sci & Technol Sch Comp Sci & Engn Nanjing Peoples R China Hefei Univ Technol Sch Management Hefei Peoples R China Univ Warwick Dept Comp Sci Coventry England Nanjing Univ Posts & Telecommun Sch Comp Sci Nanjing Peoples R China St Petersburg State Univ Grad Sch Management St Petersburg Russia

Spectral clustering and matrix factorization are two widely utilized algorithms for community detection. On the one hand, most existing spectral clustering algorithms focus on learning node representations from a well-designed similarity matrix that thoroughly incorporates data attribute information. However, they often overlook the intrinsic attribute information embedded within the algorithm itself. On the other hand, the node representations generated by most existing matrix factorization algorithms often exhibit a lack of linear independence, leading to the presence of redundant information. Motivated by them, we propose an algorithm, SOCD (Selective Orthogonalization for Community Detection), which leverages the orthogonality loss of the lanczos algorithm to monitor whether eigenvalues converge or not, and saves the already converged eigenpairs, then the corresponding converged eigenvectors are employed for community structure detection. Meanwhile, the already converged eigenvectors continue to be orthogonalized against the lanczos vector to preserve the orthogonality of the lanczos algorithm. A large number of experiments conducted on real datasets with community labels demonstrate the superiority of our algorithm over its competitors. The experimental code is available for download at https://***/AnonSimRank/SOCD/.

关键词： Community detection lanczos algorithm Spectral clustering Selective orthogonalization Dimensionality reduction

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Using an uncontracted inter-molecular basis to assess the convergence of contracted inter-molecular bases when computing the spectrum of H2O-CO

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MOLECULAR PHYSICS 2025年

作者： Wang, Xiao-Gang Carrington, Tucker Queens Univ Chem Dept Kingston ON K7L 3N6 Canada

We report energy levels of H $ _2 $ 2O-CO computed with a large product contracted (PC) basis. Intra-molecular levels are obtained using a large basis of products of contracted intra-molecular functions and contracted inter-molecular functions. To determine the size of the contracted inter-molecular basis required to achieve convergence, we compute inter-molecular levels without contracting the inter-molecular basis. We call this a $ \vert v, L \rangle $ |v,L > basis. We find that a large contracted inter-molecular basis is necessary. Previous calculations with a smaller inter-molecular basis have convergence errors similar to those caused by using the rigid-monomer approximation. For example, the largest relative splitting error is 37%. Owing to the size of the inter-molecular basis, a quadrature-point intermediate matrix $ \boldsymbol {F} $ F, rather than a DVR-point intermediate matrix $ \boldsymbol {F} $ F, and MPI parallelisation are important for reducing the calculation time.

关键词： Vibrational spectroscopy Van der Waals complexes contracted bases lanczos algorithm

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N-sided polygonal cell-based smoothed finite element method (nCS-FEM) based on Wachspress shape function for modal analysis

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2024年 159卷 434-451页

作者： Zhao, Jingui Liu, Guirong Huo, Shuhao Wang, Gang Jiang, Chen Li, Zirui Hebei Univ Technol Sch Mech Engn Tianjin 300401 Peoples R China Univ Cincinnati Dept Aerosp Engn & Engn Mech Cincinnati OH 45221 USA Taiyuan Univ Technol Coll Aeronaut & Astronaut Taiyuan 030024 Peoples R China Cent South Univ Sch Traff & Transportat Engn Key Lab Traff Safety Track Minist Educ Changsha 410076 Peoples R China

In this article, an n-sided polygonal cell-based smoothed finite element (nCS-FEM) based on the Wachspress shape function is formulated for free and forced vibration of solid structures. Cell-based smoothing domains are constructed in n-sided polygonal element mesh. Using the gradient smoothing technique, the computation of the strain-displacement matrix requires only the value of the Wachspress shape function, not the derivatives of the shape function or the mapping relationship. The lanczos algorithm is used to solve eigenvalue problems that produces vibration modes of a given structure, and the vibration modes and modal superposition techniques are used to obtain transient dynamic responses of structures subjected to arbitrary dynamics forces. The nCS-FEM is applied to solve a number of solid structures for modal analysis and compared with the Polygonal FEM, nES-FEM and ABAQUS, it is found that nCS-FEM has high precision, high efficiency and super convergence.

关键词： Smoothed finite element method CS-FEM Wachspress shape function lanczos algorithm Modal superposition technique Polygonal elements

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A lanczos-like method for non-autonomous linear ordinary differential equations

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BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA 2023年第1期16卷 81-102页

作者： Giscard, Pierre-Louis Pozza, Stefano Univ Littoral Cote dOpale UR 2597 LMPA Lab Math Pures & Appl Joseph Liouville F-62100 Calais France Charles Univ Prague Fac Math & Phys Prague 8 Czech Republic

The time-ordered exponential is defined as the function that solves a system of coupled first-order linear differential equations with generally non-constant coefficients. In spite of being at the heart of much system dynamics, control theory, and model reduction problems, the time-ordered exponential function remains elusively difficult to evaluate. The *-lanczos algorithm is a (symbolic) algorithm capable of evaluating it by producing a tridiagonalization of the original differential system. In this paper, we explain how the *-lanczos algorithm is built from a generalization of Krylov subspaces, and we prove crucial properties, such as the matching moment property. A strategy for its numerical implementation is also outlined and will be subject of future investigation.

关键词： lanczos algorithm Matrix differential equations Time-ordered exponential Matching moments Tridiagonal matrices Ordinary differential equations

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An Approach Inspired by Quantum Mechanics for the Modeling of Large Power Systems

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IEEE TRANSACTIONS ON POWER SYSTEMS 2024年第1期39卷 1360-1369页

作者： Guichard, Pierrick Retiere, Nicolas Mayou, Didier Univ Grenoble Alpes Inst NEEL CNRS F-38042 Grenoble France Univ Grenoble Alpes CNRS Grenoble INP G2Elab F-38000 Grenoble France

The ever increasing complexity of power systems mandates a further improvement of the numerical methods used for their simulation. We propose a new approach that is inspired by an exact analogy with quantum mechanics, but requires no specific knowledge of quantum physics. This approach allows in particular to use local methods commonly applied in quantum mechanics, such as lanczos' algorithm. It is applied to computing the load flow and extended to simple dynamic studies where the nodes are described by swing equations. The first set of results are for an ideal 2D-lattice grid to illustrate the method and its main features. Then a contingency analysis by the proposed approach is performed for various realistic power systems, including a model of the European network. This demonstrates the interest of the new approach and its efficiency when compared with state-of-the-art methods, especially for large power system.

关键词： Load flow local approach lanczos algorithm Hamiltonian formalism contingency analysis

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Numerical Solution of Partial Symmetric Generalized Eigenvalue Problems in Piezo Device Modal Analysis

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COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION 2025年第3期7卷 1002-1015页

作者： Muratova, Galina V. Martynova, Tatiana S. Oganesyan, Pavel A. Southern Fed Univ Vorovich II Inst Math Mech & Comp Sci Rostov Na Donu 344090 Russia

We demonstrate how different computational approaches affect the performance of solving the generalized eigenvalue problem (GEP). The layered piezo device is studied for resonance frequencies using different meshes, sparse matrix representations, and numerical methods in COMSOL Multiphysics and ACELAN-COMPOS packages. Specifically, the matrix-vector and matrix-matrix product implementation for large sparse matrices is discussed. The shift-and-invert lanczos method is used to solve the partial symmetric GEP numerically. Different solvers are compared in terms of the efficiency. The results of numerical experiments are presented.

关键词： Partial symmetric generalized eigenvalue problem (GEP) Modal analysis lanczos algorithm

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Quantum state complexity meets many-body scars

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JOURNAL OF PHYSICS-CONDENSED MATTER 2024年第15期36卷 155601-155601页

作者： Nandy, Sourav Mukherjee, Bhaskar Bhattacharyya, Arpan Banerjee, Aritra Jozef Stefan Inst Ljubljana SI-1000 Slovenia UCL Dept Phys & Astron Gower St London WC1E 6BT England Indian Inst Technol Gandhinagar Gandhinagar 382355 Gujarat India Birla Inst Technol & Sci Pilani Campus Jhunjhunu 333031 Rajasthan India Okinawa Inst Sci & Technol 1919-1 Tancha Onna Son Okinawa 9040495 Japan

Scar eigenstates in a many-body system refers to a small subset of non-thermal finite energy density eigenstates embedded into an otherwise thermal spectrum. This novel non-thermal behaviour has been seen in recent experiments simulating a one-dimensional PXP model with a kinetically-constrained local Hilbert space realised by a chain of Rydberg atoms. We probe these small sets of special eigenstates starting from particular initial states by computing the spread complexity associated to time evolution of the PXP hamiltonian. Since the scar subspace in this model is embedded only loosely, the scar states form a weakly broken representation of the Lie algebra. We demonstrate why a careful usage of the forward scattering approximation (FSA), instead of any other method, is required to extract the most appropriate set of lanczos coefficients in this case as the consequence of this approximate symmetry. Only such a method leads to a well defined notion of a closed Krylov subspace and consequently, that of spread complexity. We show this using three separate initial states, namely |Z2⟩,|Z3⟩ and the vacuum state, due to the disparate classes of scar states hosted by these sectors. We also discuss systematic methods of remedying the imperfections in the FSA setup stemming from these approximate symmetries.

关键词： quantum dynamics quantum many-body scars Rydberg atoms Krylov complexity lanczos algorithm quantum complexity

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Orthogonal polynomials on a class of planar algebraic curves

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STUDIES IN APPLIED MATHEMATICS 2023年第1期151卷 369-405页

作者： Fasondini, Marco Olver, Sheehan Xu, Yuan Univ Leicester Sch Comp & Math Sci Leicester England Imperial Coll Dept Math London England Univ Oregon Dept Math Eugene OR USA

We construct bivariate orthogonal polynomials (OPs) on algebraic curves of the form y(m) =phi(x) in R-2 where m= 1, 2 and phi is a polynomial of arbitrary degree.., in terms of univariate semiclassical OPs. We compute connection coefficients that relate the bivariate OPs to a polynomial basis that is itself orthogonal and whose span contains the OPs as a subspace. The connection matrix is shown to be banded and the connection coefficients and Jacobi matrices for OPs of degree 0,.,. N are computed via the lanczos algorithm in O (Nd-4) operations.

关键词： lanczos algorithm orthogonal polynomials

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