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The phrase "accelerating the multiplication of" is correct and usable in written English.
It can be used in contexts where you want to express the idea of speeding up the process of increasing quantity or growth.
Example: "The new technology is accelerating the multiplication of data across various platforms."
Alternatives: "speeding up the growth of" or "hastening the increase of".
Exact(2)
And there were the body's own carcinogens, hormones that switch on at certain times of life, accelerating the multiplication of cells and increasing the likelihood of mutations.
Thus, NECA increases regeneration by accelerating the multiplication of new β-cells, rather than inducing β-cell neogenesis.
Similar(58)
by accelerating the joining of small contigs.
One common criticism of contemporary psychiatry has to do with the multiplication of mental disorders.
As I suspect Corbyn does, I mistrust the multiplication of wartime commemorations.
DDI still appeared to be holding down the multiplication of the virus, he said.
The drugs work by inhibiting the multiplication of rapidly dividing cells.
His purpose was to assist in the multiplication of quantities that were then called sines.
The multiplication of (216).
It is incredibly difficult to fix the multiplication of bad mistakes.
⊗ denotes the multiplication of quaternion.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com