第三节 分块矩阵.pptVIP免费

1第三节2对于规模较大,零较多或局部比较特殊的矩阵,为了简化运算，经常采用分块法，把大矩阵分割成小矩阵.在运算时,把这些小矩阵当作元素一样来处理.具体做法是：将矩阵用若干条纵线和横线分成许多个小矩阵，每一个小矩阵称为A的子块，以子块为元素的形式上的矩阵称为分块矩阵.3bbaaA110101000001,321BBB例A001aba110000b1101B2B3B即4bbaaA110101000001,4321CCCCA1a1C002C10010a3Cbb11004C即5bbaaA110101000001bbaaA110101000001,BEOA,4321AAAAaaA01其中bbB111001E0000O0101aA其中1012aA1003bAbA10046分块矩阵的运算规则那末列数相同的行数相同与其中,,ijijBA.11111111srsrssrrBABABABABAsrsrsrsrBBBBBAAAAA11111111,(1)分块矩阵A与B的行数相同,列数相同,采用相同的分块法,有7那末为数设,,(2)1111srsrAAAAA.1111srsrAAAAA由于矩阵的加法与数乘比较简单，一般不需用分块计算。8分块成矩阵为矩阵为设,,)3(nlBlmA,,11111111trtrststBBBBBAAAAA那末的行数的列数分别等于其中,,,,,,,2121jtjjtiiiBBBAAAsrsrCCCCAB1111.),,1;,,1(1rjsiBACkjtkikij其中9,1011012100100001A例1设,0211140110210101B.AB求解分块成把BA,,1EAOEA,222111BBEBB则2221111BBEBEAOEAB.2212111111BABBAEB10.2212111111BABBAEBAB又21111BBA1101...