The phrase "attempt to approximate" is correct and usable in written English.
You can use it when discussing efforts to get close to a certain value, idea, or representation.
Example: "In our research, we will attempt to approximate the results of the previous study using a different methodology."
Alternatives: "try to estimate" or "make an effort to reach".
In my protagonist's words, "A film has to convey its message by images and relatively few words; it has little tolerance for irony or tergiversations" -- although, he continues, "through images film conveys a vast amount of information that words can only attempt to approximate.... Approximation is precious in itself, because it bears the author's stamp".
Editors attempt to approximate the original format of a document.
Nor did there seem to be any particular attempt to approximate styles or mediums.
These games range in content from the ridiculous and banal to the educational, and attempt to approximate the televised game for contestants at home.
Anthony's arrival in February 2011 was a move to shift the balance of power, his pairing with Amar'e Stoudemire an attempt to approximate Boston's firepower.
In some respects, for the masses of grownups seeking mates, either for a night or for life, dating is an attempt to approximate the collegiate condition — that surfeit both of supply and demand, of information and authentication.
Like virtual reality, these books are attempts to approximate real life, although on the written page not on computers.
As Matthew Dear, he mostly sounds like Hot Chip, or a similar indie band dorkishly and archly attempting to approximate dance music.
Since IDA is computationally intensive, a number of previous studies have attempted to approximate IDA curves using pushover analysis.
Like other cooks of this variety, Bertie managed to keep to herself whatever it was that made her creations subtly and definitely better than any attempts to approximate them (the secret ingredient).
He attempted to approximate the sound of Phillips's manzarene by deploying a small squad of backing musicians; his take is an airy jumble of glockenspiel, mandolin, horns, and percussion.
