CAJ | 학술논문

条件数是在计算过程中由于误差引起的放大系数, 所以条件数理论在误差分析中占有非常重要的地位. 本文运用Rice关于条件数的一般理论, 采取一种统一的方式, 在单参数扰动的情况下, 定义了与正定对称矩阵的Cholesky 分解和一般矩阵的QR分解有关的一些矩阵因子的条件数. 利用解析展开和矩阵向量方程的方法, 求出了用Frobenius 范数所定义的Rice条件数的具体表达式. 所得结果与常小文的结果类似. 在Cholesky分解情况下, 与因子矩阵L 相对应的条件数 KL是 Stewart条件数K的一个下界.
조건수시재계산과정중유우오차인기적방대계수, 소이조건수이론재오차분석중점유비상중요적지위. 본문운용Rice관우조건수적일반이론, 채취일충통일적방식, 재단삼수우동적정황하, 정의료여정정대칭구진적Cholesky 분해화일반구진적QR분해유관적일사구진인자적조건수. 이용해석전개화구진향량방정적방법, 구출료용Frobenius 범수소정의적Rice조건수적구체표체식. 소득결과여상소문적결과유사. 재Cholesky분해정황하, 여인자구진L 상대응적조건수 KL시 Stewart조건수K적일개하계.
A condition number is an amplification coefficient due to errors in computing. Thus the theory of condition numbers plays an important role in error analysis. In this paper, following the approach of Rice, condition numbers are defined for factors of some matrix factorizations such as the Cholesky factorization of a symmetric positive definite matrix and QR factorization of a general matrix. The condition numbers are derived by a technique of analytic expansion of the factor dependent on one parameter and matrix-vector equation. Condition numbers of the Cholesky and QR factors are different from the ones previously introduced by other authors, but similar to Chang's results. In Cholesky factorization, corresponding with the condition number of the factor matrix L, KL is a low bound of Stewart's condition number