r - Solving a system of unknowns in terms of unknowns -


i trying solve 5x5 cholesky decomposition (for variance-covariance matrix) in terms of unknowns (no constants).

a simplified version, sake of giving example, 2x2 decomposition:

[[a,0],[b,c]]*[[a,b],[0,c]]=[[u1,u2],[u2,u3]]

is there software (i'm proficient in r, if r can great) solve above yield answer of left-hand variables in terms of right-hand variables? i.e. final answer:

a = sqrt(u1) b = u2/sqrt(u1) c = sqrt(u3+u2/u1)

take @ this wikipedia section.

the symbolic definition of (i,j)th entry of decomposition defined recursively in terms of entries above , left. implement these recursions using matlab's symbolic math toolbox , apply them (symbolically) obtain formulas 5x5 case. warned you'll end extremely complicated formulas of unknowns, , - excepting unusual circumstances - fine implement decomposition iteratively fixed size 5x5 matrix.


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