This is a special case for LU factorization (𝑈=𝐿𝑇).
𝐴=𝐿𝐿𝑇
where

  • 𝐴 , by 𝑚×𝑛, is SPD

2x2 example

𝐿=[𝑥𝑦0𝑧] 𝐿𝑇=[𝑥0𝑦𝑧]

so

𝐴=𝐿𝐿𝑇=[𝑥2𝑥𝑦𝑥𝑦𝑦2+𝑧2]

Costs

Only lower triangular part of 𝐴 is accessed, so only 12 the storage is required.
Only 𝑛36 multiplications and additions required, so 12 the work of LU factorization
No need to pivoting