《结构工程中的数学方法》课程教学课件（讲稿）Cholesky_alternative_procedure

2AlgebraicproblemsinmatrixformSystemsof LinearEquationsDetermination of matrices L* and D.operationsCi*tobuildstructure of matricesL*and Dthe first column of L* and D0[d, =ad1i=2.....n-d,00·sequence of operations C.*to build.电columnsjof L*andD,j=2,...n-1d, = a, -2d0000.0：[5 -(a -~d ), = 1,00Dj = 2,...,n-100：operation C,*to build the element d,0>C,: d, =an-2’d62aMichael Beer, Engineering Mathematics

Michael Beer, Engineering Mathematics Systems of Linear Equations 2 Algebraic problems in matrix form 62a Determination of matrices L* and D ● sequence of operations Cij * to build columns j of L* and D, j = 2, ., n−1 ( ) j 1 * 2 j jj jk k k 1 * ij j 1 * * * ij ij ik jk k k 1 j d a ld C : 1 l a l l d , i j 1,.,n d j 2,.,n 1 − = − =   = − ∑       = − =+ ∑   = − » ● operations Ci1 * to build the first column of L* and D 1 11 * i1 * i1 i1 1 d a C : a l , i 2,.,n d  =   = =   » ● operation Cn * to build the element dn n 1 * * 2 n n nn nk k k 1 C : d a l d − = » = − ∑ * 21 * * * i1 ij *** n1 n j n n 1 1 0 0 . . 0 l 1 0 . 1 0 l . l 1 0 0 1 0 l . l . l 1 −     =   L       1 i n d 0 . 0 . 0 0 0 0 d 0 . 0 0 . 0 0 0 0 0 . 0 . 0 d     =   D        ● structure of matrices L* and D