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Total Least Squares algorithm for Errors-in-Variables Systems: Iterative algorithm or two-step algorithm

IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 10753-10763页

作者： Chen, Jing Na, Jing Li, Junhong Zhu, Quanmin Jiangnan Univ Sch Sci Wuxi 214122 Peoples R China Kunming Univ Sci & Technol Fac Mech & Elect Engn Kunming 650550 Peoples R China Nantong Univ Sch Elect Engn Nantong 226019 Peoples R China Univ West England Sch Engn Bristol BS16 1QY England

The total least squares (TLS) algorithm is a superior identification tool for low-order errors-in-variables (EIV) systems, where the estimate can be obtained by solving an eigenvector of the minimum eigenvalue of an augmented matrix. However, the TLS algorithm demonstrates inefficiency when applied to high-order EIV systems. This study introduces two innovative TLS algorithms: an iterative TLS algorithm, offering superior performance for low-order EIV models, and a two-step TLS algorithm, designed to effectively handle high-order EIV models. In comparison to the conventional TLS algorithm, these proposed methodologies present noteworthy advantages, including: 1) reduced computational costs, 2) the utilization of an iterative technique to calculate the inverse, and 3) the diversification of EIV identification methods. Simulation bench test examples are selected to show the efficacy of the proposed algorithms and transparent procedure for applications.

关键词： Eigenvalues and eigenfunctions Mathematical models Noise Computational modeling Convergence Iterative algorithms Large-scale systems Cost function Automation Accuracy Errors-in-variables system total least squares iterative algorithm two-step algorithm eigenvalue calculation

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Comparison of the STANDARD M10 C. difficile, Xpert C. difficile, and BD MAX Cdiff assays as confirmatory tests in a two-step algorithm for diagnosing Clostridioides difficile infection

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MICROBIOLOGY SPECTRUM 2025年第1期13卷 e0166224页

作者： Choi, Hyunseul Kang, Minhee Yun, Sun Ae Yu, Hui-Jin Suh, Eunsang Kim, Tae Yeul Huh, Hee Jae Lee, Nam Yong Smart Healthcare Res Inst Biomed Engn Res Ctr Samsung Med Ctr Seoul South Korea Samsung Biomed Res Inst Ctr Clin Med Samsung Med Ctr Seoul South Korea Seoul Med Ctr Dept Lab Med Seoul South Korea Sungkyunkwan Univ Samsung Med Ctr Sch Med Dept Lab Med & Genet Seoul South Korea

Current guidelines recommend a two-step algorithm rather than relying solely on a single test for diagnosing Clostridioides difficile infection. This algorithm starts with enzyme immunoassay (EIA) for detecting glutamate dehydrogenase (GDH) and toxins A/B, followed by nucleic acid amplification test (NAAT) for GDH-positive but toxin-negative cases. This study compared the performance of three commercial NAATs: the STANDARD M10 C. difficile, Xpert C. difficile, and BD MAX Cdiff assays, utilized as confirmatory testing of the two-step algorithm. two hundred archived stool specimens, previously tested GDH-positive but toxin-negative by EIA, were analyzed in parallel with these NAATs and toxigenic culture, which served as the reference standard. Sensitivity, specificity, positive predictive value, and negative predictive value were 89.1%, 92.6%, 94.6%, and 85.2%, respectively, for the M10 assay;95.8%, 86.4%, 91.2%, and 93.3%, respectively, for the Xpert assay;and 89.8%, 91.4%, 93.8%, and 86.0%, respectively, for the BD MAX assay. The rates of invalid results were 1.0%, 0.5%, and 1.0% for the M10, Xpert, and BD MAX assays, respectively. In conclusion, the M10 assay is a reliable diagnostic tool, performing comparably to the Xpert and BD MAX assays when used as confirmatory testing in the two-step algorithm.

关键词： Clostridioides difficile M10 Xpert BD MAX two-step algorithm

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two-step algorithm for the Automated Analysis of Fluorescent Microscopy Data in Biomedical Applications 2

Two-step Algorithm for the Automated Analysis of Fluorescent...

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2nd IEEE International Conference on Control in Technical Systems (CTS)

作者： Markelov, Oleg A. Bogachev, Mikhail I. Pyko, Nikita S. Kayumov, Airat R. St Petersburg Electrotech Univ Radio Syst Dept St Petersburg Russia Kazan Fed Univ Inst Fundamental Med & Biol Dept Genet Kazan Russia

ISBN: (纸本)9781538607770

Measurement automation is essential in various biomedical and biotechnological applications become increasingly important with their intensification and wide utilization. Estimation of both pro-and eukaryotic cells sub-populations in different cultures, samples and tissues, including differentiation of live and dead bacterial cells, stem cells in eukaryotic cell culture and so on are essential in multiple biomedical and biotechnological applications. Fluorescent microscopy is a widely used methodology to obtain the above estimates. Wide utilization of biotechnologies increases the importance of automatic microscopic image processing tools design aiming at both qualitative and quantitative assessment of cells sub-populations. Existing methods are mostly based either on cell detection and counting or on the statistical analysis of image areas with similar staining. However, these methods exhibit known drawbacks including their inapplicability to the communities of cells adherent to each other and to external surfaces with biofilms being a prominent example. Another limitation of standard image processing tools in their high level of automation limiting the ability of the operator to adjust the algorithm parameters to particular microscopic imaging conditions as well as to specific features of the studied cells sub-populations. Here we present a two-step algorithm including preliminary adjustment of its parameters to the imaging conditions based on several representative images from the studied cohort in the first step and fully automated analysis of a large series of images with fixed algorithm parameters in the second step. Out results indicate that the suggested methodology is barely sensitive to the decision threshold value that allows to reduce the parameterization of the algorithm.

关键词： fluorescent microscopy two-step algorithm measurement automation cell staining

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An efficient two-step algorithm for the stationary incompressible magnetohydrodynamic equations

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APPLIED MATHEMATICS AND COMPUTATION 2017年 302卷 21-33页

作者： Wu, Jilian Liu, Demin Feng, Xinlong Huang, Pengzhan Xinjiang Univ Coll Math & Syst Sci Urumqi 830046 Peoples R China

A new highly efficient two-step algorithm for the stationary incompressible magnetohydro-dynamic equations is studied in this paper. The algorithm uses a lower order finite element pair (i.e., P(1)b-P-1-P-1) to compute an initial approximation, that is using the Mini-element (i.e., P(1)b-P-1) to approximate the velocity and pressure and P-1 element to approximate the magnetic field, then applies a higher order finite elethent pair (i.e., P-2-P-1-P-2) to solve a linear system on the same mesh. Furthermore, the convergence analyses of standard Galerkin finite element method and the two-step algorithm are addressed. Lastly, numerical experiments are presented to verify both the theory and the efficiency of the algorithm. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Stationary incompressible magnetohydrodynamic equations two-step algorithm Finite element method Convergence analyses

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A new two-step algorithm for ionospheric tomography solution

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GPS SOLUTIONS 2012年第1期16卷 89-94页

作者： Wen, Debao Wang, Yong Norman, Robert Changsha Univ Sci & Technol Sch Traff & Transportat Engn Changsha 410004 Hunan Peoples R China Henan Polytech Univ Sch Surveying & Land Informat Engn Jiaozuo 454000 Peoples R China RMIT Univ Ctr Satellite Positioning & Nav Melbourne Vic 3001 Australia

Ionospheric tomography inverse algorithms are usually an ill-conditioned problem because the geometric distribution of continuously operating reference GPS stations is not ideal for this task. In order to cope with such ill-conditioning, a new tomographic algorithm, termed two-step algorithm (TSA), is presented. The electron density is estimated in two steps: Phillips smoothing method (PSM) is first used to resolve the ill-conditioned problem in the ionospheric tomography system, and then, the PSM solution is input as an initial value to the multiplicative algebraic reconstruction technique (MART) and iteratively improved. Numerical simulations using the International Reference Ionosphere 2007 model demonstrate that the TSA is applicable to GPS-based ionospheric tomography reconstruction and is superior to PSM and MART when these techniques are used alone. The new algorithm is applied to reconstruct the ionospheric electron density distribution over China using GPS observations, and a comparison with ionosonde observations is made.

关键词： Computerized ionospheric tomography Total electron content Ionospheric electron density Ill-conditioned two-step algorithm MART

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An efficient two-step algorithm for steady-state natural convection problem

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2016年 101卷 387-398页

作者： Wu, Jilian Huang, Pengzhan Feng, Xinlong Liu, Demin Xinjiang Univ Coll Math & Syst Sci Urumqi 830046 Peoples R China

In this paper, we propose a new highly efficient two-step algorithm based on local Gauss integration for the 2D steady-state natural convection problem. The basic idea of the algorithm is to compute an initial approximation for the velocity, pressure and temperature based on a lowest equal-order finite element pair P-1-P-1-P-1, then to solve a linear system based on a quadratic equal-order finite element pair P-2-P-2-P-2 on the same mesh. Next, we give the corresponding stability and convergence of the algorithm, which show that the new two-step algorithm has the same order convergence rate as the quadratic equal-order stabilized finite element method. Finally, some numerical examples show that the new method is efficient, reliable, has good precision and can save a lot of computational time compared with the quadratic equal-order stabilized method. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Natural convection problem two-step algorithm Equal-order element Local Gauss integration Stability and convergence

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A two-step algorithm for solving singular linear systems with index one

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APPLIED MATHEMATICS AND COMPUTATION 2006年第1期175卷 472-485页

作者： Zhou, Jieyong Wei, Yimin Fudan Univ Dept Math Shanghai 200433 Peoples R China Shanghai Univ Finance & Econ Dept Appl Math Shanghai 200433 Peoples R China Shanghai Jiao Tong Univ Dept Math Shanghai 200240 Peoples R China

In this paper, a two-step algorithm for solving singular linear systems is presented. We compare this algorithm with a DGCR type algorithm [A. Sidi, A unified approach to Krylov subspace methods for the Drazin-inverse solution of singular non-symmetric linear systems, Linear Algebra Appl. 298 (1999) 99-113] by numerical experiments. An error analysis is given. (c) 2005 Elsevier Inc. All rights reserved.

关键词： iterative methods DGMRES two-step algorithm singular linear system Drazin inverse index

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A rapid two-step algorithm detects and identifies clinical macrolide and beta-lactam antibiotic resistance in clinical bacterial isolates

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JOURNAL OF MICROBIOLOGICAL METHODS 2014年 102卷 26-31页

作者： Lu, Xuedong Nie, Shuping Xia, Chengjing Huang, Lie He, Ying Wu, Runxiang Zhang, Li Guangdong Med Coll Futian Hosp Dept Lab Med Shenzhen 518033 Peoples R China Uppsala Univ Biomed Ctr Dept Cell & Mol Biol SE-75124 Uppsala Sweden

Purpose: Aiming to identify macrolide and beta-lactam resistance in clinical bacterial isolates rapidly and accurately, a two-step algorithm was developed based on detection of eight antibiotic resistance genes. Methods: Targeting at genes linked to bacterial macrolide (msrA, ermA, ermB, and ermC) and beta-lactam (bla(TEM), bla(SHV), bla(CTX-N-1), bin(CTX-M-9)) antibiotic resistances, this method includes a multiplex real-time PCR, a melting temperature profile analysis as well as a liquid bead microarray assay. Liquid bead microarray assay is applied only when indistinguishable T-m profile is observed. Results: The clinical validity of this method was assessed on clinical bacterial isolates. Among the total 580 isolates that were determined by our diagnostic method, 75% of them were identified by the multiplex real-time PCR with melting temperature analysis alone, while the remaining 25% required both multiplex real-time PCR with melting temperature analysis and liquid bead microarray assay for identification. Compared with the traditional phenotypic antibiotic susceptibility test, an overall agreement of 81.2% (kappa = 0.614, 95% Cl = 0550-0.679) was observed, with a sensitivity and specificity of 87.7% and 73% respectively. Besides, the average test turnaround time is 3.9 h, which is much shorter in comparison with more than 24 h for the traditional phenotypic tests. Conclusions: Having the advantages of the shorter operating time and comparable high sensitivity and specificity with the traditional phenotypic test, our two-step algorithm provides an efficient tool for rapid determination of macrolide and beta-lactam antibiotic resistances in clinical bacterial isolates. (C) 2014 Elsevier B.V. All rights reserved.

关键词： two-step algorithm Antibiotic resistance genes Clinical bacterial isolates

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A REFINED two-step algorithm FOR HIGH RESOLUTION SPACEBORNE SAR WITH SQUINTED SLIDING SPOTLIGHT MODE

A REFINED TWO-STEP ALGORITHM FOR HIGH RESOLUTION SPACEBORNE ...

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IEEE International Geoscience and Remote Sensing Symposium (IGARSS)

作者： Kuang, Hui Chen, Jie Yang, Wei Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China

ISBN: (纸本)9781479979295

Spaceborne squinted sliding spotlight synthetic aperture radar (SAR) can achieve high-resolution image with well flexibility. However, traditional imaging algorithm cannot focus its data, as the serious coupling between the range and the azimuth and the azimuth spectral aliasing problem. To process the data, a refined two-step algorithm is proposed in this paper. Firstly, the linear range cell migration correction (LRCMC) and De-rotation are adopted to solve the azimuth spectral aliasing problem. Then the data is focused with a modified wavenumber domain algorithm (WDA). Also, the azimuth nonlinear chirp scaling (NCS) method is used to solve the limited depth-of-azimuth-focus (DOAF) problem. At last, the geometric correction is adopted to correct the geometrical distortion. The computer simulation results verify the validity of the proposed imaging algorithm.

关键词： SAR squinted sliding spotlight mode azimuth NCS two-step algorithm high resolution

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Improved two-step algorithm in Geosynchronous SAR

Improved Two-Step Algorithm in Geosynchronous SAR

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IET International Radar Conference

作者： W. Yang Z. Ding Y. Zhu C.Ni C. Hu School of Information and Eletronic Beijing Institute of Technology Chinese Academy of Space Technology

ISBN: (纸本)9781629931340

In Geosynchronous Synthetic Aperture Radar (GEO SAR),the very large swath width makes the classical line trajectory model invalid and the imaging parameters space-variant. In this paper, an accurate slant range model is firstly given for GEO SAR. Next, an improved two-step algorithm which can overcome the difficulties introduced by space-variance of imaging parameters is proposed. Furthermore, simulation results fully verify the correctness and effectiveness of the derived algorithm.

关键词： slant range model GEO SAR two-step algorithm

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