We derive necessary and sufficient conditions for the simple eigenvalues of rational matrix functions with symmetry structure to have the same normwise condition number with respect to arbitrary and structure-preserving perturbations. We obtain an exact expression for the structured condition number of simple eigenvalues of symmetric, skew-symmetric and T-even/odd rational matrix functions, and tight bounds are obtained for simple eigenvalues of Hermitian, skew-Hermitian, & lowast;-even/odd, & lowast;-palindromic and T-palindromic rational matrix functions.

In this paper, we compute the structured eigenvalue backward error of a Rosenbrock system matrix $ S(z)=\left [\begin {smallmatrix} A-zI & B \\ C & P(z) \end {smallmatrix} ight ] $ S(z)=[A-zIBCP(z)] for a given scalar $ \lambda \in {\mathbb C} $ lambda is an element of C. We have developed simplified formulas for the structured eigenvalue backward error of the Rosenbrock system matrix, considering both full and partial block perturbations. These formulas involve computing structured & micro;-values of a rectangular matrix under rectangular-block-diagonal perturbations. For the reformulated & micro;-value problem, we provide an explicit expression using partial isometric matrices and also obtain a computable upper bound, which is equal to the & micro;-value when the perturbation matrix has no more than three blocks at the diagonal. The results are illustrated through numerical experiments.

We study linear time-invariant dissipative Hamiltonian differential-algebraic systems. We characterize when the systems are robustly asymptotically stable and derive exact conditions and bounds when this property is lost under structure-preserving perturbations.

The three-step alternating iteration scheme for finding an iterative solution of a singular (non-singular) linear systems in a faster way was introduced by Nandi et al. [Numer. Algorithms; 84 (2) (2020) 457-483], recently. The authors then provided its convergence criteria for a class of matrix splitting called proper G-weak regular splittings of type I. In this note, we analyze further the convergence criteria of the same scheme. In this aspect, we obtain sufficient conditions for the convergence of the same scheme for another class of matrix splittings called proper G-weak regular splittings of type II. We then show that this scheme converges faster than the two-step alternating and usual iteration schemes, even for this class of splittings. As a particular case, we also establish faster convergence criteria of three-step in a nonsingular matrix setting. This is shown that a large amount of computational time and memory are required in single-step and two-step alternating iterative methods to solve the nonsingular linear systems more efficiently than the three-step alternating iteration method. Finally, the semiconvergence of a three-step alternating iterative scheme is established. Its faster semiconvergence is demonstrated by considering a singular linear system arising from the Markov process.

The stability and large-scale production of perovskite solar cells depend on their manufacture ability under ambient conditions rather than a glovebox. The presence of defect states within the perovskite film is crucial in influencing the performance of solar cells. This study explores the effectiveness of copper(I) halide additives in mitigating the impact of defect states in the MAPbI3-based perovskite material. The findings of the study reveal that the inclusion of an ideal quantity of copper(I) halide additives in perovskite solar cells leads to a notable improvement in the performance when compared with the pristine MAPbI3-based perovskite. The analysis of time-resolved photoluminescence, transient photocurrent, and photovoltage indicates an extended lifespan of photogenerated charge carriers and their improved collection by the electrodes. The inclusion of copper(I) halide additives in perovskite solar cells results in a significant 24% boost in the short-circuit current density (J sc), leading to an overall improvement in their performance (PCE) by 17%.

We address the problem of computing the eigenvalue backward error of the Rosenbrock system matrix under various types of block perturbations. We establish novel characterizations of these backward errors using a class of minimization problems involving the sum of two generalized Rayleigh quotients (SRQ2). For computational purposes and analysis, we reformulate such optimization problems as minimization of a rational function over the joint numerical range of three Hermitian matrices. This reformulation eliminates certain local minimizers of the original SRQ2 minimization and allows for convenient visualization of the solution. Furthermore, by exploiting the convexity within the joint numerical range, we derive a characterization of the optimal solution using a nonlinear eigenvalue problem with eigenvector dependency (NEPv). The NEPv characterization enables a more efficient solution of the SRQ2 minimization compared to traditional optimization techniques. Our numerical experiments demonstrate the benefits and effectiveness of the NEPv approach for SRQ2 minimization in computing eigenvalue backward errors of Rosenbrock systems.

In this paper, we consider linear time-invariant continuous control systems which are bounded real, also known as scattering passive. Our main theoretical contribution is to show the equivalence between such systems and port-Hamiltonian (PH) systems whose factors satisfy certain linear matrix inequalities. Based on this result, we propose a formulation for the problem of finding the nearest bounded-real system to a given system, and design an algorithm combining alternating optimization and Nesterov's fast gradient method. This formulation also allows us to check whether a given system is bounded real by solving a semidefinite program, and provide a PH parametrization for it. We illustrate our proposed algorithms on real and synthetic data sets.

For a given set Ω⊆ℂ, a matrix pair (E,A) is called Ω-admissible if it is regular, impulse-free and its eigenvalues lie inside the region Ω. In this paper, we provide a dissipative Hamiltonian characterization for the matrix pairs that are Ω-admissible where Ω is an LMI region. We then use these results for solving the nearest Ω-admissible matrix pair problem: Given a matrix pair (E,A), find the nearest Ω-admissible pair (Ẽ, Ã) to the given pair (E,A). We illustrate our results on several data sets and compare with the state of the art.

We study linear time-invariant Dissipative Hamiltonian (DH) systems arising in energy-based modeling of dynamical systems. An advantage of DH systems is that they are always stable due to the structure of their coefficient matrices, and, under further weak conditions, even asymptotically stable. In this paper, we discuss the computation of the stability radii for a given asymptotically stable DH system; i.e., the smallest structured perturbation that puts a DH system on the boundary of the region of asymptotic stability, so that it has purely imaginary eigenvalues. We obtain explicit computable formulas for various structured stability radii. For this, the problem of computing stability radii is reformulated in terms of minimizing the Rayleigh quotient of a Hermitian matrix or the sum of two generalized Rayleigh quotients of Hermitian semidefinite matrices. This reformulation results in the problem of minimizing the largest eigenvalue of an eigenvector-dependent Hermitian matrix or minimizing the smallest eigenvalue of a Hermitian matrix which depends on the eigenvector. It is also demonstrated (via numerical experiments) that, under structure-preserving perturbations, the asymptotic stability of a DH system is much more robust than under general perturbations, since the distance to instability is typically much larger when structure-preserving perturbations are considered. Finally, similar results are obtained for optimally robust representations of stable systems.

In this paper, we provide a dissipative Hamiltonian (DH) characterization for the set of matrices whose eigenvalues belong to a given LMI region. This characterization is a generalization of that of Choudhary et al. (Numer. Linear Algebra Appl., 2020) to any LMI region. It can be used in various contexts, which we illustrate on the nearest $\Omega$-stable matrix problem: given an LMI region $\Omega \subseteq \mathbb{C}$ and a matrix $A \in \mathbb{C}^{n,n}$, find the nearest matrix to $A$ whose eigenvalues belong to $\Omega$. Finally, we generalize our characterization to more general regions that can be expressed using LMIs involving complex matrices.

Spiro‐OMeTAD is a commonly used organic hole‐transport material (HTM) in MAPbI3‐based perovskite solar cells (PSCs) for achieving high efficiency. However, its hydrophilic nature compromises device stability and performance reproducibility, especially under ambient conditions. In this study, PSCs are fabricated under ambient conditions, and phase‐pure iron pyrite nanocrystals (FeS2 NCs) are synthesized and utilized as HTM. Using iron pyrite as the HTM leads to a 22% increase in device short‐circuit current density (JSC) compared to Spiro‐OMeTAD, resulting in enhanced PSC performance. This confirms FeS2 NCs as a promising HTM for PSCs. Iron pyrite improves the extraction of photogenerated charge carriers compared to Spiro‐OMeTAD, indicating a superior extraction layer. Furthermore, the longer stability of the iron pyrite layer under humid conditions is compared to the Spiro‐OMeTAD layer, as demonstrated by contact angle measurements. This improvement helps prevent humidity‐induced degradation of the perovskite layer. Transient photocurrent studies under reverse bias conditions reveal fewer defects at the perovskite/iron pyrite interface, suggesting a defect passivation effect of FeS2 NCs. This study demonstrates that iron pyrite can serve as an effective HTM to enhance the performance and stability of low‐cost PSCs fabricated under ambient conditions.

From a wider perspective, the functioning of perovskite-based optoelectronic devices such as solar cells, light-emitting diodes, transistors, and sensors is hugely dependent on the material fabrication of a perovskite active layer, integrating this active layeFrom a wider perspective, the functioning of perovskite-based optoelectronic devices such as solar cells, light-emitting diodes, transistors, and sensors is hugely dependent on the material fabrication of a perovskite active layer, integrating this active layer in the appropriate device architecture and optimizing the device performance by altering various components. An in-depth understanding of the structure-property correlation is, therefore, a key factor for the development of this technology, particularly for industrial large-scale applications. This study aims to comprehend the effect of the material fabrication modifications done at a macroscale, providing insights into the microscale charge-carrier dynamics. Micrograins larger than 100 mu m were achieved for the poly(methyl methacrylate) (PMMA)-incorporated triple-cation perovskite precursor with compact film morphology without any antisolvent treatment. A detailed investigation of the crystallization dynamics is strived for. Enhancement in the radiative recombination lifetime from 0.88 mu s (for the pristine FAMACs film) to 1.45 mu s for the FAMACs film through PMMA incorporation, devoid of any antisolvent treatment, was achieved. Additionally, we appraised our microstructural findings of the photoactive layer against the operating conditions in a device by means of transient photocurrent measurements, aiming for a deeper understanding of the polymer-in-perovskite approach for precursor development.r in the appropriate device architecture and optimizing the device performance by altering various components. An in-depth understanding of the structure-property correlation is, therefore, a key factor for the development of this technology, particularly for industrial large-scale applications. This study aims to comprehend the effect of the material fabrication modifications done at a macroscale, providing insights into the microscale charge-carrier dynamics. Micrograins larger than 100 mu m were achieved for the poly(methyl methacrylate) (PMMA)-incorporated triple-cation perovskite precursor with compact film morphology without any antisolvent treatment. A detailed investigation of the crystallization dynamics is strived for. Enhancement in the radiative recombination lifetime from 0.88 mu s (for the pristine FAMACs film) to 1.45 mu s for the FAMACs film through PMMA incorporation, devoid of any antisolvent treatment, was achieved. Additionally, we appraised our microstructural findings of the photoactive layer against the operating conditions in a device by means of transient photocurrent measurements, aiming for a deeper understanding of the polymer-in-perovskite approach for precursor development.

In the literature, asymptotic expansions for certain approximate solutions of operator equations and eigenvalues associated with Green's kernel are not justified in the case of iterated collocation method for piecewise polynomial space of degree >= 2. In this paper, we prove the existence of asymptotic expansion of operator equations at partition points and for a simple eigenvalue associated with Green's type kernel. A numerical example is considered to illustrate theoretical results.

Over the past decade, there has been a pronounced research emphasis on leveraging the advantageous defect states inherent in metal dichalcogenide nanostructures to intricately modulate and tailor their optoelectronic characteristics. Here, we demonstrate how defects significantly impact the linear and nonlinear optical properties of pristine FeS2 nanomaterials (NMs), ionic liquids (DMII) passivated FeS2 NMs, and CoFeS2 NMs. These NMs were synthesized using a low-cost hot-injection process, and their structure was validated via X-ray diffraction analysis. The oval-like structure of the NMs is revealed by high-resolution transmission electron microscopy, and X-ray photoelectron spectra demonstrate the presence of the divalent oxidation state of iron (Fe) and cobalt (Co). After the treatment of DMII on the pristine NMs, a decrease in the Urbach energy (E-u) was found, with values reducing from 0.77 to 0.27 meV. This phenomenon may potentially be associated with the passivation of surface imperfections in pristine NMs. The treatment of DMII further enhances the lifetime of charge carriers (1.25 ns) and conductivity by one order compared to pristine FeS2 NMs. On the other hand, introducing Co in FeS2 alters the conductivity of pure FeS2 NMs, shifting them from p-type to n-type and significantly enhancing their electrical characteristics by 3 orders of magnitude. The open aperture z-scan study revealed that the CoFeS2 NMs have an effective nonlinear absorption coefficient (beta(eff)) of 160 cm GW(-1), which is superior to that of the pristine NMs with a beta(eff) of 130 cm GW(-1). The optical limiting threshold value (1.01 J cm(-2)) of CoFeS2 NMs is much higher than those of both pristine and DMII-treated FeS2 NMs, indicating superior optical limiting performance. The current work presents a comprehensive analysis of pristine, DMII-treated, and Co-alloyed FeS2 NMs, focusing on their potential for linear and nonlinear optoelectronic applications.

We derive computable formulas for the structured backward errors of a complex number λ when considered as an approximate eigenvalue of rational matrix functions that carry a symmetry structure. We consider symmetric, skew-symmetric, Hermitian, skew-Hermitian, * -palindromic, T-even, T-odd, * -even, and * -odd structures. Numerical experiments show that the backward errors with respect to structure-preserving and arbitrary perturbations are significantly different.

The efficiency of organic solar cells (OSCs) has been improved more than 19% recently with the development of non-fullerene acceptor materials. Further improvement is still attainable with the optimal combinations of do-nors and acceptors that provide minimal energy losses. In this work, a data-enabled machine-learning (ML) framework was employed to predict the energy losses in the polymer:non-fullerene acceptor based devices. Based on the collected experimental dataset, the prediction accuracies of various machine learning models were sys-tematically compared by estimating mean absolute percentage errors (MAPE), root mean squared errors (RMSE), and person's r coefficient. The Random Forest regression model showed the best performance in predicting the energy losses with a correlation coefficient of 0.83 and relative error in the range of 0 - 20%. The predictive ability of this model was further validated using the different parameters of devices with power conversion efficiency range of 6 - 18%. Three different donor-acceptor combinations were chosen for fabricating the photovoltaic devices to fit this model into practical devices and experimentally obtained energy loss values were compared with the predicted values. In addition, the device parameters with the molecular descriptors to un-derstand the correlation and energy loss is highly correlated with the HOMO offset. This study demonstrates that the ML approach provide an effective method to predict and virtual screen of promising donor-acceptor pairs with minimal energy loss and would be useful for developing next-generation high performance solar cell materials.

Although doping has the potential to improve the performance of organic photovoltaic cells (OPVc), doping effects on charge transport, recombination, and energetic disorder are still obscure. Doping has two opposing effects: on the one hand, dopant ions create more trap centers, while free dopant‐induced charges fill deep states, potentially providing better performance. The optimum amount of dopants can considerably improve the performance of OPVc. Herein, the energetic distribution of trap states in P3HT: PC71BM‐based OPVc doped with iron pyrite nanocubes (NCs) is reported. Using the reverse bias transient photocurrent (TPC) measurement, the energetic trap distributions with different doping conditions are studied. The photovoltaic characteristics and TPC phenomena of the OPVc greatly improve through doping. Variations in trap distributions with doping levels are analyzed to interpret the obtained trap density of states profiles. The light‐dependent current–voltage characteristics help to identify the presence of a less trap‐assisted recombination process in the optimum device. This study highlights the mechanism for performance improvement in devices with optimal doping of iron pyrite NCs.

Detailed understanding of the various influences of deposition conditions on the structure–property relationship for spray-coated polymer films is crucial for their scalable device applications. In the present study, the influences of in-situ substrate temperature and acoustic substrate vibration on the charge carrier dynamics of poly(3-hexylthiophene) and [6,6]-phenyl-C71-butyric acid methyl ester (P3HT:PC71BM) based ultrasonic spray-coated polymer solar cells have been investigated thoroughly by employing Impedance spectroscopy, Mott–Schottky analysis, Urbach energy analysis, and trap-state density estimations. The device prepared under the influences of in-situ substrate temperature and acoustic substrate vibration shows more than three times enhancement in PCE (3.24%) compared to that of the reference one (0.9%). A correlation between charge transport behaviour and deposition conditions has been identified for the devices. The surface roughness and rigid droplet boundaries were found to set major performance limitations. The overall resistance of the devices was found to get decreased by 70% whilst the global charge carrier mobility was found to get increased from 6.09 × 10–5 to 9.43 × 10–4 cm2 V−1 s−1 with the simultaneous application of substrate temperature and acoustic vibration, forming uniform and homogeneous films with much reduced surface roughness and droplet boundaries compared to the untreated reference devices. Systematic variation in the trap and defect-state densities were also observed. The trap-state density reduced from 5.03 × 1015 to 2.71 × 1015 cm−3 after the combined treatment of in-situ annealing and substrate vibration. Urbach energy was found to be 218.4 meV for the untreated active layer, which reduced to 177.2 meV for the active layer treated with in-situ-annealing and acoustic substrate vibration. The superior electrical properties achieved by optimizing the active layer morphology using different spray deposition conditions led to around four times enhancement in device efficiency.

We study the structured distance to singularity for a given regular matrix pencil $A+sE$, where $(A,E)\in \mathbb S \subseteq (\mathbb C^{n,n})^2$. This includes Hermitian, skew-Hermitian, $*$-even, $*$-odd, $*$-palindromic, T-palindromic, and dissipative Hamiltonian pencils. We present a purely linear algebra-based approach to derive explicit computable formulas for the distance to the nearest structured pencil $(A-\Delta_A)+s(E-\Delta_E)$ such that $A-\Delta_A$ and $E-\Delta_E$ have a common null vector. We then obtain a family of computable lower bounds for the unstructured and structured distances to singularity. Numerical experiments suggest that in many cases, there is a significant difference between structured and unstructured distances. This approach extends to structured matrix polynomials with higher degrees.