:ѹľLDLֽ(ֻԶԳƾ)

ʽ:CompressDecompositionLDL(A,Index)

A:ñľ(˾Ϊ1Ϊ1),ԪδԭԳƾǲ
Index:ԽԪAеλ(0ʼ)

˵:

1ִϷAȴķֽõľ

2Ϊ󲿷Է鶼һԳϡ跽,Ϊ˽Լڴ,һñķʽԾݽд,⡣þǶԾȽLDLֽ,Ȼ⡣֮Եдɷֱֽ,Ϊʱľ󲻱,ǵʽұߵĳ,ʱΪ˷ֹÿһη̾ͷֽLDLһ,Ǻܲǵ,һԷֽٶε÷ֽõL뷽ԽԼɱ.

ԭ:øĽƽ(Cholesky)зֽ

ο:ܳ.ֵ̳[M].ߵȽ,,2009:186-187

:

A =
[ 4.0000    1.0000    0.0000    0.0000    0.0000    0.0000
  1.0000    6.0000    3.0000    2.0000    0.0000    0.0000
  0.0000    3.0000    5.0000    2.0000    3.0000    0.0000
  0.0000    2.0000    2.0000    4.0000    0.0000    1.0000
  0.0000    0.0000    3.0000    0.0000    7.0000    0.0000
  0.0000    0.0000    0.0000    1.0000    0.0000    2.0000 ]

ҪϵĶԳƾALDLֽ,ΪǱ,Ҵǲ,ִ

a=[4, 1, 6,3,5,2,2,4,3,0,7,1,0,2];//洢ǲ
c=[0,    2,  4,    7,    10,  13];//ԽԪaе
l=CompressDecompositionLDL(a,c)//سõµķֽ
l =
[ 4.00000000000000    0.25000000000000    5.75000000000000    0.52173913043478    3.43478260869565    0.34782608695652    0.27848101265822    3.03797468354430    0.87341772151898   -0.27500000000000    4.15000000000000    0.32916666666666    0.06626506024096    1.65261044176707 ]
