:ѹľLLֽ(ֻԶԳƾ)

ʽ:CompressDecompositionLL(A,Index)

A:ñľ(˾Ϊ1Ϊ1),ԪδԭԳƾǲ
Index:ԽԪAеλ(0ʼ)

˵:

1ִϷAȴķֽõľ

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

ԭ:ƽ(Cholesky)зֽ

ο:ܳ.ֵ̳[M].ߵȽ,,2009:185-186

:

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 ]

ҪϵĶԳƾALLֽ,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=CompressDecompositionLL(a,c)//سõµķֽ
l =
[ 2.00000000000000    0.50000000000000    2.39791576165636    1.25108648434245    1.85331665095192    0.83405765622829    0.51611349773344    1.74297868132238    1.61871960652763   -0.47931913736365    2.03715487874634    0.57373048260195    0.13499219076029    1.28553896936929 ]