Shares of Rocket Fuel and FireEye hewed close to their names on the first day of trading, taking off to atmospheric heights in their initial public offerings.

Rocket Fuel, an advertising technology company that relies on artificial intelligence, opened at $59.95 in their first day of trading on Friday, more than double their initial public offering price, and then jumped as high as $62.50.

Minutes later, shares in FireEye, a cybersecurity services provider, opened at $40.30, doubling their I.P.O. price of $20.

The companies priced either at the top of an already-increased price range, as in Rocket Fuel’s case, or well above a heightened range, as FireEye had done.

By the end of trading, Rocket Fuel closed at $56.10, while FireEye closed at $36.

Investors and deal makers are betting on a resurgence of technology I.P.O.’s by year-end, after the sector stayed abnormally quiet for much of the year. As of last week, technology offerings composed just 17 percent of all new stock sales, a five-year low.

FireEye’s chief executive, David DeWalt, said in an interview that the company may actually have been helped a bit by the paucity in new stock offerings, garnering extra attention from prospective shareholders.

“A tremendous amount of due diligence was going into: is this real or is it not?” he said in an interview. “As the investors studied these assets, in the depth I was seeing, they were realizing how important this was and how powerful this model was.”

According to bankers who arrange I.P.O.’s, one important attraction for a would-be debutante is either exceptional growth rates or a unique position. According to Rocket Fuel’s chief executive, George John, potential investors in the start-up saw both in his company, which relies on computer programs that quickly learn which ads succeed in drawing in the most customers and on which sites.

In its most recent prospectus, Rocket Fuel reported a 138 percent growth in revenue between 2011 and 2012, to $106.6 million.

“The reception for ad tech companies has not been great,” Mr. John said in an interview. “We were betting that investors will give us credit for our growth.”

Rocket Fuel trades on the Nasdaq market under the ticker symbol “FUEL.” FireEye is trading on the Nasdaq under the symbol “FEYE.”