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In this article, we focus on solving a sequence of linear systems that have identical (or similar) coefficient matrices. For this type of problem, we investigate subspace correction (SC) and deflation methods, which use an auxiliary matrix (subspace) to accelerate the convergence of the iterative method. In practical simulations, these acceleration methods typically work well when the range of the auxiliary matrix contains eigenspaces corresponding to small eigenvalues of the coefficient matrix. We develop a new algebraic auxiliary matrix construction method based on error vector sampling in which eigenvectors with small eigenvalues are efficiently identified in the solution process. We use the generated auxiliary matrix for convergence acceleration in the following solution step. Numerical tests confirm that both SC and deflation methods with the auxiliary matrix can accelerate the solution process of the iterative solver. Furthermore, we examine the applicability of our technique to the estimation of the condition number of the coefficient matrix. We also present the algorithm of the preconditioned conjugate gradient method with condition number estimation. [ABSTRACT FROM AUTHOR]

Abstract: The Asian citrus psyllid, Diaphorina citri Kuwayama (Hemiptera: Liviidae), is a major citrus pest that transmits the bacteria Candidatus Liberibacter asiaticus and Ca. L. americanus associated with huanglongbing (HLB) disease. Diaphorina citri population densities can affect the effectiveness of its monitoring and sampling methods. Thus, we compared different methods for adult D. citri monitoring in groves with and without insecticide application programmes. Four short‐term experiments were carried out, each one lasting four consecutive weeks. In these experiments, sticky cards with different colours (yellow, light green, green and dark green), sweep net, two suction device models, visual inspection and stem tap sampling were assessed. Two long‐term experiments were conducted for 4.5 and 5 years, in which only yellow sticky card and visual inspection for D. citri monitoring were assessed. For the short‐term experiments, psyllids were detected by all monitoring methods during all sampling periods in areas without chemical control. However, in areas with psyllid control via fortnightly and monthly applications of insecticides, only sticky cards, regardless of their colour, were able to detect the presence of D. citri. Similarly, for the long‐term experiments, yellow sticky cards were more effective than visual inspection for detecting and quantifying D. citri in all areas with or without insecticide application. Therefore, in areas where HLB is present and chemical control of psyllid is required, sticky cards are the most reliable option for monitoring D. citri. [ABSTRACT FROM AUTHOR]