In an instance of agreement, the proper spelling is the same everywhere in the English-speaking world: improvise. It means to speak without preparation or invent something using the materials at hand.
One can also be an improviser, though this form does have an alternate spelling improvisor. However, the er spelling is vastly more common.
Something can be improvisatory, and the art form of creating a scene on stage without a script is usually called improv. The correct term, however, is improvisation.
However, the actress says that the western dance helps her to improvise and fine tune skills as a dancer. [Times of India]
Welcome to Suspects, an hour-long, case-of-the-week police procedural for Channel Five that’s unique in that the dialogue is completely improvised. [The Guardian]
With his clunky spreadsheet, the restaurant owner was improvising a version of the software that large chains use to schedule employees at strict intervals, and to end their shifts when business slows. [The New Yorker]
I am sure that somewhere out there in the vast netherworld of the Internet there is an explanation of how a sonic screwdriver actually works, but let’s be honest — thematically, it is a magic wand. Most of the time, the Doctor just waves it around, it makes whistling noises, and he improvises. [Huffington Post]
Being an improviser – as Tallis almost inevitably was, himself – Robson arranged the hymns to accommodate concise solos or dialogues. [Sydney Morning Herald]
It helps tremendously that Bruno is a skilled improvisor and his castmates know how to roll with what he gives them. [Twin Cities Daily Planet]
Some dances, including the first solo (by Sara Mearns), had a wild, improvisatory, part-stumbling, part-inspired quality. [New York Times]
Huw Tregelles Williams talks to Olivier Latry about his international career and uncovers the secrets of the French tradition of improvisation. [South Wales Evening Post]
By day, Isaac Rodriguez is the CEO of the Provident Loan Society, the 180-year-old nonprofit lender that was founded by business tycoons including J.P. Morgan and Cornelius Vanderbilt. By night, Rodriguez performs as an improv comedian with Artistic New Directions, a theater group in Manhattan. [Metro]