Fastest way to perform A * B * A’

eveningsilverfox
Tue, 23 Jul 2024 13:10:29 +0000
General Usage

Given two dense square matrices with ComplexF64 elements of size approximately 100000X100000, A and B, what is the fastest way to perform R=ABA’, where A’=conj(tr(A)) is the Hermitian conjugate of A?.

If it helps:
(1) A=inv(I-X), where I is the identity matrix and X is another dense matrix.
(2) A and B are not necessarily Hermitian.
(3) Eventually, I need only a certain small sub-block of the result R, for instance, R[10:11,12:13].

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