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Thank you very much for your answer !
I managed to use the accelerate SparseSolve "Objective C" API from a C++ program.
Just in case it maybe useful for other readers, the header files (e.g. Sparse/Solve.h) contain a lot of detailed comments and documentation.
More examples would be nice though ;)
On my first test cases, the Sparse Cholesky solver is 3-4 times faster than UMFPACK used in Julia (in double) on my M1 Max machine : great !
It seems to be sequential (110 % of CPU and 0%GPU): is it possible to improve further the performance with multi-threading ?