吉林大学学报（理学版）
吉林大學學報（理學版）
길림대학학보（이학판）
JOURNAL OF JILIN UNIVERSITY(SCIENCE EDITION)
2014年
3期
413-420
,共8页
薛秋芳%高兴宝%刘晓光
薛鞦芳%高興寶%劉曉光
설추방%고흥보%류효광
H-矩阵%Gauss-Seidel迭代法%外推Gauss-Seidel迭代法%最优尺度矩阵%谱半径
H-矩陣%Gauss-Seidel迭代法%外推Gauss-Seidel迭代法%最優呎度矩陣%譜半徑
H-구진%Gauss-Seidel질대법%외추Gauss-Seidel질대법%최우척도구진%보반경
H-matrix%Gauss-Seidel iterative method%extrapolated Gauss-Seidel iterative method%optimally scaled matrix%spectral radius
考虑外推 Gauss-Seidel 迭代法的收敛性及其与 H-矩阵的关系，给出了外推 Gauss-Seidel迭代法与Jacobi迭代法收敛性的关系及收敛的参数范围。利用最优尺度矩阵及M-1N的估计量给出了H-矩阵外推Gauss-Seidel法谱半径的上界估计式，并基于外推Gauss-Seidel及Gauss-Seidel迭代法得到一般 H-矩阵的等价条件。
攷慮外推 Gauss-Seidel 迭代法的收斂性及其與 H-矩陣的關繫，給齣瞭外推 Gauss-Seidel迭代法與Jacobi迭代法收斂性的關繫及收斂的參數範圍。利用最優呎度矩陣及M-1N的估計量給齣瞭H-矩陣外推Gauss-Seidel法譜半徑的上界估計式，併基于外推Gauss-Seidel及Gauss-Seidel迭代法得到一般 H-矩陣的等價條件。
고필외추 Gauss-Seidel 질대법적수렴성급기여 H-구진적관계，급출료외추 Gauss-Seidel질대법여Jacobi질대법수렴성적관계급수렴적삼수범위。이용최우척도구진급M-1N적고계량급출료H-구진외추Gauss-Seidel법보반경적상계고계식，병기우외추Gauss-Seidel급Gauss-Seidel질대법득도일반 H-구진적등개조건。
The convergence performance of the extrapolated Gauss-Seidel iterative method and its relationship with H-matrix were discussed.The convergence relationship between the extrapolated Gauss-Seidel and the Jacobi iterative methods and also the range of the extrapolated parameter when the method converges were given. The upper bound estimates for the spectral radius of the extrapolated Gauss-Seidel iterative method were obtained by using the optimally scaled matrix and the estimator of M-1 N. Meanwhile, equivalent conditions for general H-matrices based on the extrapolated Gauss-Seidel and the Gauss-Seidel iterative methods were provided.
