人民长江
人民長江
인민장강
YANGTZE RIVER
2014年
13期
37-39
,共3页
秩亏自由网%极小范数解%特征值%正交向量
秩虧自由網%極小範數解%特徵值%正交嚮量
질우자유망%겁소범수해%특정치%정교향량
rank defect free network%small norm solution%eigenvalue%orthogonal vector
在经典测量平差中,按间接平差法列出的误差方程系数阵为列满秩,所得到的法方程系数阵为一个对称的满秩矩阵,法方程组具有唯一解。而当控制网中没有必要的起算数据时,则按间接平差法所列出的误差方程系数阵是非列满秩的,其对应的法方程系数阵也是一个秩亏的奇异阵。探讨了秩亏自由网的法方程系数阵的一种解算方法。
在經典測量平差中,按間接平差法列齣的誤差方程繫數陣為列滿秩,所得到的法方程繫數陣為一箇對稱的滿秩矩陣,法方程組具有唯一解。而噹控製網中沒有必要的起算數據時,則按間接平差法所列齣的誤差方程繫數陣是非列滿秩的,其對應的法方程繫數陣也是一箇秩虧的奇異陣。探討瞭秩虧自由網的法方程繫數陣的一種解算方法。
재경전측량평차중,안간접평차법렬출적오차방정계수진위렬만질,소득도적법방정계수진위일개대칭적만질구진,법방정조구유유일해。이당공제망중몰유필요적기산수거시,칙안간접평차법소렬출적오차방정계수진시비렬만질적,기대응적법방정계수진야시일개질우적기이진。탐토료질우자유망적법방정계수진적일충해산방법。
In classical adjustment, the normal equations have a unique solution if the error equation coefficient matrix achieved by indirect adjustment is a full column rank, and the normal equation coefficient matrix achieved by the same method is a sym-metrical full rank matrix. When there is no necessary initial data in control network, the error equation coefficient matrix by indi-rect adjustment is a non-full column rank and the corresponding normal equation is also a rank deficient singular matrix. The paper discusses the solution for normal equation coefficient matrix in the rank defect free network.