矩阵的条件数 当一个方程组由于初始数据的小扰动而使解严重失真时,称之为病忑 坏条件的)方程组,反之,称之为良态(好条件的)方程组。通常 用方程组系数矩阵A的条件数来刻画方程组的这种性态 cond(4)=1|4r1 > help cond COND Condition number with respect to inversion COND(X returns the 2-norm condition number (the ratio of the largest singular value of X to the smallest). Large condition numbers indicate a nearly singular matrix COND(X, P)returns the condition number of X in P-norm NORMX, P)*NORM(INVOX), P) Where p=1.2 inf or ' fro Question: What is the singular value of a matrix? 兰州大学信息科学与工程学院 矩阵理论第8讲4兰州大学信息科学与工程学院 矩阵理论第8讲-4 矩阵的条件数 – 当一个方程组由于初始数据的小扰动而使解严重失真时，称之为病态 （坏条件的）方程组，反之，称之为良态（好条件的）方程组。通常 用方程组系数矩阵A的条件数来刻画方程组的这种性态 >> help cond COND Condition number with respect to inversion. COND(X) returns the 2-norm condition number (the ratio of the largest singular value of X to the smallest). Large condition numbers indicate a nearly singular matrix. COND(X,P) returns the condition number of X in P-norm: NORM(X,P) * NORM(INV(X),P). where P = 1, 2, inf, or 'fro‘ 1 cond( ) A A A− = 