Convergence on Gauss-Seidel iterative methods for linear systems with general H-matrices

It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible $H-$matrices (generalized strictly diagonally dominant matrices) and Hermitian positive definite matrices. But, the same is not necessarily true for linear systems with nonstrictly diagonally dominant matrices and general $H-$matrices. This paper firstly proposes some necessary and sufficient conditions for convergence on Gauss-Seidel iterative methods to establish several new theoretical results on linear systems with nonstrictly diagonally dominant matrices and general $H-$matrices. Then, the convergence results on preconditioned Gauss-Seidel (PGS) iterative methods for general $H-$matrices are presented. Finally, some numerical examples are given to demonstrate the results obtained in this paper

Morphology, DNA Phylogeny, and Pathogenicity of Wilsonomyces carpophilus Isolate Causing Shot-Hole Disease of Prunus divaricata and Prunus armeniaca in Wild-Fruit Forest of Western Tianshan Mountains, China

Prunus divaricata and Prunus armeniaca are important wild fruit trees that grow in part of the Western Tianshan Mountains in Central Asia, and they have been listed as endangered species in China. Shot-hole disease of stone fruits has become a major threat in the wild-fruit forest of the Western Tianshan Mountains. Twenty-five isolates were selected from diseased P. divaricata and P. armeniaca. According to the morphological characteristics of the culture, the 25 isolates were divided into eight morphological groups. Conidia were spindle-shaped, with ovate apical cells and truncated basal cells, with the majority of conidia comprising 3–4 septa, and the conidia had the same shape and color in morphological groups. Based on morphological and cultural characteristics and multilocus analysis using the internal transcribed spacer (ITS) region, partial large subunit (LSU) nuclear ribosomal RNA (nrRNA) gene, and the translation elongation factor 1-alpha (tef1) gene, the fungus was identified as Wilsonomyces carpophilus. The 25 W. carpophilus isolates had high genetic diversity in phylogenetic analysis, and the morphological groups did not correspond to phylogenetic groups. The pathogenicity of all W. carpophilus isolates was confirmed by inoculating healthy P. divaricata and P. armeniaca leaves and fruits. The pathogen was re-isolated from all inoculated tissues, thereby fulfilling Koch’s postulates. There were no significant differences in the pathogenicity of different isolates inoculated on P. armeniaca and P. divaricata leaves (p > 0.05). On fruit, G053 7m3 and G052 5m2 showed significant differences in inoculation on P. armeniaca, and G010 5m2 showed extremely significant differences with G004 7m2 and G004 5m2 on P. divaricata (p < 0.05). This is the first report on shot-hole disease of P. armeniaca (wild apricot) leaves and P. divaricata induced by W. carpophilus in China