If $A, B, C$ are $n\times n$ matrices, with $B$ and $C$ nonsingular, and $b$ is a vector of size $n$, how would you determine $x = B^{-1} (2A+I)(C^{-1}+A)b$, without computing the inverses of matrices. How many operations will this computation require?
2026-04-14 07:45:12.1776152712
Inverse of Matrices
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Do:
where "solve $Gy=c$" reads "solve the system $Gy=c$ by any suitable means", e.g., by using the LU factorisation.
The cost is determined essentially by the cost of the solve, which generally is $O(n^3)$.