perfektionieren
to perfect
To improve something so that it becomes perfect, flawless, or as good as possible.
Sie hat jahrelang geübt, um ihre Technik am Klavier zu perfektionieren.
She practiced for years to perfect her piano technique.

to perfect
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to perfect
To improve something so that it becomes perfect, flawless, or as good as possible.
Sie hat jahrelang geübt, um ihre Technik am Klavier zu perfektionieren.
She practiced for years to perfect her piano technique.

The verb 'perfektionieren' (to perfect) belongs to the word family of 'perfekt' (perfect, adjective) and 'die Perfektion' (perfection, noun). The ending '-ieren' turns the stem into a verb, as with many words of Latin origin.
Er arbeitet an der Perfektion seiner Methode.
He is working on the perfection of his method.
Verbs ending in '-ieren' form the past participle without the prefix 'ge-'. So it is 'hat perfektioniert' (has perfected), not 'hat geperfektioniert'. This is a common mistake.
Der Künstler hat seine Technik über viele Jahre perfektioniert.
The artist perfected his technique over many years.
'Perfektionieren' (to perfect) is a transitive verb and always needs an accusative object. You always perfect something.
Die Köchin will ihr neues Rezept perfektionieren.
The chef wants to perfect her new recipe.
to improve
'verbessern' and 'perfektionieren' both describe making something better. 'verbessern' is neutral and general: something becomes better than before. 'perfektionieren' is stronger. It means that you want to make something as good as possible, almost without mistakes. The word fits especially well when there is already a good foundation and you are working on the final details. So you can improve something without perfecting it.

Für den Wettbewerb perfektioniert Tom jeden Abend seine Technik.
For the competition, Tom perfects his technique every evening.
Sie verbessert den Plan, damit die Reise für alle einfacher wird.
She improves the plan so that the trip will be easier for everyone.