纺织高校基础科学学报
紡織高校基礎科學學報
방직고교기출과학학보
BASIC SCIENCES JOURNAL OF TEXTILE UNIVERSITIES
2013年
4期
511-515
,共5页
双对角占优矩阵%对角占优矩阵%等对角占优矩阵%ρ(A-1 )下界
雙對角佔優矩陣%對角佔優矩陣%等對角佔優矩陣%ρ(A-1 )下界
쌍대각점우구진%대각점우구진%등대각점우구진%ρ(A-1 )하계
double equidiagonal dominant matrix%diagonally dominant matrix%equidiagonally dominant matrix%lower bound of ρ(A-1 )
研究严格双对角占优矩阵A在一定条件下,ρ(A-1)下界的一种新估计。对满足n≥ k ≥ i ≥1的任意k ,i ,有| akk |-Rk ≤| ai |-Ri ,进而得到新的下界min i≠ j| aj |+ Ri (A)| ai × aj |- Ri (A)× Rj (A)。并且证明这种新的估计要比已存在的下界更精确。最后用数值例子说明了这个结论的有效性。
研究嚴格雙對角佔優矩陣A在一定條件下,ρ(A-1)下界的一種新估計。對滿足n≥ k ≥ i ≥1的任意k ,i ,有| akk |-Rk ≤| ai |-Ri ,進而得到新的下界min i≠ j| aj |+ Ri (A)| ai × aj |- Ri (A)× Rj (A)。併且證明這種新的估計要比已存在的下界更精確。最後用數值例子說明瞭這箇結論的有效性。
연구엄격쌍대각점우구진A재일정조건하,ρ(A-1)하계적일충신고계。대만족n≥ k ≥ i ≥1적임의k ,i ,유| akk |-Rk ≤| ai |-Ri ,진이득도신적하계min i≠ j| aj |+ Ri (A)| ai × aj |- Ri (A)× Rj (A)。병차증명저충신적고계요비이존재적하계경정학。최후용수치례자설명료저개결론적유효성。
The estimations of the lower bound of ρ(A-1 ) is discussed when matrix A is under a certain conditions and A is a strictly doubly diagonally dominant matrix .T he |akk|-Rk≤ |ai |-Ri of every k ,i subjected to n≥ k≥ i≥1 is obtained .Further the new lower bound min i≠ j| aj |+ Ri (A)| ai × aj |- Ri (A) × Rj (A) is received .It is proved that this new estimations is better than the lower existing bound ,and the numercial example illustrates the effectiveness of the criteria .