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1、1.1 LLT 算法11.2 LDLT 算法1LLT算法LL八T算法1.2.3.4.5.6.一7.8.9.1().11.10.11.12.13.14.15.一16.17.18.1().12.for j = 1 : nfor A- = 1 : j 1for i = j + 1 : n hj = hj l/kljk cndforendforfor i j i n hj =%/务endfor13. endforFor y = 1 ： nd = A i JJFor i=j+i : nI = AEnd for iFor k=1 ：y-1d = d -I I dJ i jk jk kFor j=j+i ：
2、nI = I -I I dij ij ik jk kEnd for iEnd for kFor+i ：/ = I IdEnd for iEnd for j1.1 LDLT 算法参考算法：Avoiding taking square rootsAn alternative form is the factorizationA = LDLt= (lL31A = LDLt= (lL3101320 /I L21I Dx0 0 1 L32 = l21a d3J o 0 1 7 L31A/。1+。2L31L21D1 + 1/32。2(symmetric)易 1。1+&2。2 +。3This form el
3、iminates the need to take square roots. When A is positive definite the elements of the diagonal matrix D are all positive. However this factorization canbe used for any square, symmetrical matrix.If A is real, the following recursive relations apply for the entries of D andL:J-lDj =工力- LjQk fc=lLtj
4、 = LikLjkDk I , for i j.For complex Hermitian matrix A, the following formula applies:jlDj = Ajj - LjkLkDk fc=i （儿厂 52 LikL【kD、for i j.The LDLt and LLt factorizations （note that L is different between the two） may be easily related:The last expression is the product of a lower triangular matrix and
5、its transpose, as is the LLt factorization.算法设计： /Cholesky decompositionDj =，力 - 44 k=l1 /。Lij = a厂 L诉1注2 与、fc=lfor i j.髓 wiki得到算法的伪代码A = LDLt = LD?D2Lt = LDi（D2）TLT = LD2（LD2）TFor j = ：nd = A/ JJFor z = y+ 1 : nI = AEnd ioriFor % =i遍历L第j行所有元素d = d -I I d j j jk jk kI隰定/（要提高效率需要再设个数组）1 jkFor ,= 遍历L第k列局部元素I = I -I I dij ij ik jk kEnd for/End for k以前基于ITSOL的程序没有进行效率考虑.For . 4Z = J 4- 1 :I = I /dEnd for i End for/