if speed matters you should better consider something like building a hash for array2 for simple lookups or at least a complex OR-ed regex looping just once over array2.
edit
DB<102> @data1 = ( "a 1 a", "a 2 T", "a 3 C" );
=> ("a 1 a", "a 2 T", "a 3 C")
DB<103> @data2 = ( "a 2 Y", "a 3 R", "a 4 Q", "b 5 R" );
=> ("a 2 Y", "a 3 R", "a 4 Q", "b 5 R")
DB<104> $regex = join "|" , map {/^(\w\s+\d)/} @data1
=> "a 1|a 2|a 3"
DB<105> grep { /^($regex)/ } @data2
=> ("a 2 Y", "a 3 R")
think I spotted (and corrected) a bug in your logic, you forgot to anchor to string start '^' in your grep regex.
Cheers Rolf
( addicted to the Perl Programming Language)
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