Abstract: High penetration of renewable energy brings challenges to secure and economic system operation, especially in regions with intensive seasonal hydropower and photovoltaic (PV) resources. This paper develops a cooperative game–based scheduling model integrating hydropower, PV, and thermal power into a virtual alliance. An upper-level game-theoretic pricing mechanism ensures that the grand coalition’s payoff surpasses any subcoalition, while a lower-level optimization minimizes water consumption for cascaded hydropower peak regulation. The framework incorporates power balance, ramping, reservoir, and flow constraints, solved via iterative price adjustment and particle swarm optimization. Fairness of benefit allocation is assessed through a mean deviation percentage (MDP)-based index. Case studies on the Lishui system show that the proposed strategy reduces PV and water curtailment, alleviates channel competition, and enhances both economic efficiency and alliance stability, offering practical insights for multi-energy coordination in regional markets.

Abstract: The Moore–Penrose inverse is the most popular type of matrix generalized inverses that has many applications both in matrix theory and numerical linear algebra. The Moore–Penrose inverse of a matrix can be found via singular value decomposition (abbreviated SVD) of this matrix. In this regard, there exist the most effective algorithm which consists of two phases. At the first phase an initial matrix is reduced to upper bidiagonal form (the Golub–Kahan bidiagonalization algorithm). The second phase is known as the Golub–Reinsch algorithm. This is an iterative procedure that generates a sequence of bidiagonal matrices converging to a diagonal form. Acting in this way, we obtain an iterative approximation to the SVD of bidiagonal matrix. In this paper, we develop a method that can be considered as an alternative to the Golub–Reinsch iterative procedure. By implementing an approach proposed in the work, the following two main results have been achieved. First, we obtain explicit expressions for the entries of the Moore–Penrose inverse of bidigonal matrices. Secondly, based on the closed form formulas, we get a finite recursive numerical algorithm of optimal computational complexity. Thus, in certain cases, we can compute the Moore–Penrose inverse of bidiagonal matrices without using the SVD.

Abstract: This letter presents a grid-based design framework for rotated subarray configurations to address the grating lobe (GL) suppression challenge in large-spacing arrays (element spacing $>\lambda /2$). The proposed method combines rotational subarray techniques with a constrained grid structure, achieving effective GL suppression while maintaining array modularity and reducing design complexity. By formulating the problem via iterative convex approximation, subarray positions and rotation angles are alternately optimized, achieving greater design freedom than prior methods. Numerical simulations validate the method’s superiority over conventional approaches in both GL suppression performance and structural practicality. The optimized design achieves 1 dB to 4 dB better GL suppression than existing solutions across various array configurations.

Abstract: This paper presents an iterative magnetostatic method with analytical postprocessing for calculating alternating current (AC) copper losses in hairpin-wound permanent magnet synchronous machines (PMSMs). Conventional magnetostatic solvers are accessible but cannot capture field changes from eddy currents, while transient finite element analysis (FEA) tools are often commercially restricted. The proposed method uses time-stepping magnetostatic FEA, solving multiple problems per step, with each iteration refining current distributions to account for nonlinear eddy current effects. It is compared with a standard magnetostatic method and transient FEA. Results show improved accuracy over static methods with increased computation time, providing a practical alternative to commercial transient solvers.

Abstract: Coordinated control of electric heating, ventilation, and air conditioning (HVAC) systems enhances grid flexibility but introduces significant privacy risks through smart meter data exposure and communication vulnerabilities. While distributed methods, such as the alternating direction method of multipliers (ADMM), mitigate some of these risks, iterative coordination steps remain susceptible. This paper proposes an encrypted ADMM framework utilizing Brakerski–Fan– Vercauteren (BFV) homomorphic encryption along with a secure random-chain aggregation protocol to safeguard individual building power consumption data during coordination. Co-simulation with EnergyPlus Functional Mock-up Units (FMUs) demonstrates that the approach effectively enforces global power constraints and reduces costs while maintaining user privacy against semi-honest adversaries with manageable computational overhead.

Abstract: This communication introduces a novel optimization method for designing rotated subarrays. Rotated subarrays typically employ modular configurations with large element spacing to enable cost-efficient phased array implementations. The main challenge is reducing grating lobes (GLs) caused by the large spacing, which is a complex optimization problem. By carefully redesigning the optimization model, this nonconvex problem is transformed into a convex form that can be solved efficiently. Numerical results demonstrate superior GL suppression compared to existing methods, while full-wave electromagnetic simulations validate the approach.

Abstract: The multi-coloring method can be formulated as a graph coloring problem, which is known to be NP-hard. In this study, we solve the graph coloring problem using a quadratic unconstrained binary optimization (QUBO) formulation. We perform parameter tuning and propose an iterative color reduction method to further decrease the number of colors. Finally, we evaluate the effectiveness of the resulting parallel ordering as a preprocessing step for iterative methods, compared with conventional approaches.

Abstract: This paper presents an algorithm for the iterative control of a 2D array of memory piezoactuators which are used in a novel Hysteretic Deformable Mirror (HDM) Huisman et al. (2021). The HDM is composed of a mirror thin plate placed on top of piezoelectric wafers interlaced with electrodes and exhibited output remanence behavior (e.g., the presence of remnant memory when the input is signal is set to zero). The control objective in the HDM is to achieve and hold a desired mirror surface defection by regulating the remnant output of the actuators. Following recent iterative control method to achieve desired remnant output for a single piezoactuator, we present the generalization of this approach to control the remnant output of 2D array of piezoactuators with a time-multiplexed control input. Particularly, we present conditions for the convergence of the 2D output remnant to a desired 2D reference values. We show the efficacy of our method in a simulation of an HDM with 5×5 piezoactuators.

Abstract: Abstract Achieving high-quality three-dimensional (3D) reconstruction has been a challenging problem due to factors such as motion blur. In this article, we first construct a mathematical model of an iterative relaxation method in reconstructing images, including iterative method and relaxation method. Then, the iterative image derivation model with relaxation factors is constructed by introducing relaxation factors. Next, a motion blur model based on the iterative relaxation method is proposed and combined with the 3D reconstruction method of non-coding points. Finally, the 3D reconstruction in some real scenes is carried out using the motion blur non-coded target 3D reconstruction method based on the iterative relaxation method with error analysis. The results show that the reconstruction accuracy under the optimized path has been improved by two orders of magnitude compared with that under the initial path, and the reconstruction error is basically maintained at about 0.042 mm, with the maximum not exceeding 0.05 mm. This indicates that the proposed method can effectively reduce the reconstruction error and achieve a high reconstruction accuracy. The motion blur non-coded target 3D reconstruction method based on the iterative relaxation method proposed in this article has certain practicality and promotion value.

Abstract: Abstract While limited coupled cluster theory is formally nonvariational, it is not broadly appreciated whether this is a major issue in practice . We carried out a detailed comparison with de facto full CI energies for a relatively large and diverse set of molecules near equilibrium geometries. Fully iterative limited CC methods such as CCSDT, CCSDTQ, and CCSDTQ5 do represent practical upper bounds to the FCI energy, as do CCSDT-3, CCSDTQ-3, and CCSD(cT). While quasiperturbative approaches such as CCSD(T) and especially CCSDT(Q) may significantly over-correlate molecules if there is significant static correlation, this is much less of an issue with Lambda approaches such as CCSDT(Q) Λ .

Abstract: Motivation: Radial FSE MRI is valued for motion insensitivity but requires longer acquisition times due to overlapping central k-space sampling. Optimal k-space sampling patterns for radial FSE are yet to be fully explored. Goal(s): To propose an optimal k-space sampling pattern based on PSF evaluation to improve image quality for radial FSE MRI. Approach: Simulate an radial FSE sequence, optimizing the sampling pattern by minimizing PSF differences, and evaluating image quality via NMSE against a conventional reference. Results: The proposed sampling pattern suppressed artifacts better, reducing NMSE from 0.00174 to 0.000845, with increased sampling density near the blade center and a narrower blade width. Impact: Improving acquisition speed in radial fast spin echo MRI with optimized k-space under sampling pattern and iterative reconstruction may enhance examination throughput and reduce patient burden while maintaining or enhancing image quality.

Abstract: Considering the three critical factors of data quantization, channel fading, and denial of service (DoS) attack introduced by the networked control systems (NCSs) simultaneously, we propose a novel compensatory data-driven networked iterative learning control (COMP-DDNILC) method for nonlinear repetitive NCSs under a model-free design and analysis framework. By reformulating the iterative input-and-output (I/O) dynamics of the nonlinear NCS as an iterative linear data model (iLDM), an iterative linear predictive data model (iLPDM) is developed to predict the missing data arisen from DoS attacks. Then, a relationship is built to describe the coupling effects of the three critical factors, based on which the COMP-DDNILC is designed by involving the compensatory mechanism of DoS attacks and the fading coefficient inversion to improve the control performance. The COMP-DDNILC also involves an iterative adaption mechanism to update the iLPDM to enhance the robustness against uncertainties. The data-driven nature of COMP-DDNILC makes it applicable to practical NCSs without model information available. The simulation study verifies the results.

Abstract: After the interruption of the timing service, the increase in clock offset is a critical issue for the global navigation satellite system (GNSS)-disciplined oven-controlled crystal oscillator (OCXO). Current timekeeping methods for GNSS-disciplined OCXO have some drawbacks, such as high computational complexity, inadequate consideration of temperature effects, and insufficient separation of the impacts of temperature and aging. To address this issue, this study proposes a timekeeping method using a dual iterative algorithm. First, the external iteration separates the clock offset caused by temperature and aging. Then, the internal Gauss–Seidel iterative algorithm estimates the temperature and aging coefficients. During the timing service interruption phase, the model estimates and compensates for the frequency offset in real time using the coefficients. The proposed method demonstrates improved performance compared with OCXO in the free state and compensated by a second-order polynomial model, with better accuracy, drift rate, and long-term stability. The time offset is better than 4 μs over 24 h, representing an improvement of over 95% compared with the OCXO in the free state.

Abstract: This paper introduces an iterative one-dimensional DLT framework that reconstructs instantaneous vehicle speed frame-by-frame from roadside monocular video. By leveraging wheel-rim collinearity and bidirectional inter-frame displacement averaging, the method mitigates errors induced by curved trajectories and abrupt motion changes. Field experiments covering straight-line and turning manoeuvres show a 54 % RMSE reduction versus single-pass estimation across diverse speeds and radii, confirming its robustness and accuracy for video imagebased crash-reconstruction tasks.

Abstract: This report presents a comprehensive theoretical and computational analysis of two fundamental Krylov subspace methods: the Arnoldi and Lanczos algorithms. We begin by establishing the mathematical foundation of Krylov subspaces and their properties in the context of iterative methods for large scale linear systems and eigenvalue problems. Through extensive numerical experiments, we demonstrate the practical effectiveness of both methods across various problem classes. Our results establish comprehensive guidelines for method selection based on matrix properties, problem size, and accuracy requirements, culminating in specific recommendations for implementation and optimization strategies.Keywords: Krylov subspace methods, Arnoldi iteration, Lanczos algorithm, iterative methods, numerical linear algebra, orthogonalization processes

Abstract: Abstract The temperature and humidity profiles are the basic parameters to describe the vertical structure of the atmosphere. Efficiently and accurately obtaining atmospheric profiles has always been an important premise in the study of the thermal and dynamic characteristics of the boundary layer. Aiming at this problem, this paper proposes a retrieval method by combining the physical iterative method and the Convolutional Neural Network (CNN), by which the atmospheric temperature and humidity profiles can be simultaneously retrieved based on ground‐based infrared hyperspectral observation. From the results of retrieval experiments, it can be found that the hybrid retrieval method can not only improve the retrieval accuracy of temperature and humidity profiles, but also significantly reduce time consumption compared with the physical iterative method. For the monthly statistical results of temperature, the mean bias (BIAS), and root mean‐squared error (RMSE) of the hybrid retrieval method are improved by at least 29% and 28% compared with the physical iterative method, and also show an improvement of 7% and 6% over the CNN method. The retrieval accuracy has also improved notably for humidity profiles, where compared with the physical iterative method, the BIAS is reduced by nearly 38% in October and the RMSE is reduced by nearly 35%. However, in May, both BIAS and RMSE are reduced by more than 35%. Compared with the CNN algorithm, the BIAS and RMSE of humidity decreased by 6% and 5% in September, respectively.