What is the most efficient algorithm for multiplying a square matrix by an upper triangular matrix

If A and B are square matrix, and B is an upper triangular matrix, then what is the most efficient algorithm to calculate C = A x B?

Answer 1

[Walter Roberson]

No-one knows yet what the most efficient algorithm is. This is a topic of sustained theoretical research.

https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm#Sub-cubic_algorithms

For the current best algorithm that gets to "the constant coefficient hidden by the Big O notation is so large that these algorithms are only worthwhile for matrices that are too large to handle on present-day computers". But you didn't ask about present day computers, you asked about the most efficient algorithm -- an algorithm that does not start being cost efficient until the matrix sizes are larger than the number of elementary particles in the universe would still potentially be the most efficient algorithm, even though it might be impractical for any purpose at all.