PALM BEACH GARDENS, Fla. >> This is not the rivalry anyone had in mind when Tiger Woods and Rory McIlroy began the year.

They made their debut in Abu Dhabi last month and both missed the cut. The next time they played in the same tournament was last week in the Match Play Championship, and both were eliminated in the first round.

The difference is that Woods returned to Torrey Pines the week after missing the cut. He left little reason for anyone to doubt his game when he built a lead that reached eight shots until the day dragged on and he won by four for his 75th career win on the PGA Tour.

McIlroy knew starting the year there would attention on his change from Titleist to Nike, and it only intensified with two bad results.

But the start of the Florida swing is no time to panic, and McIlroy sure didn’t sound worried at the Honda Classic.

“It’s fine,” he said. “I knew coming into (the year) it was going to be a bit of a process and I knew there was going to be comments if it didn’t happen for me right away,” McIlroy said. “I’m only two tournaments into the season. I’ve still 20 to go. So it’s not like I’m in any rush. It’s not like I’m pushing for answers. Everything is there. It’s just a matter of putting it all together.”

McIlroy put it together much sooner a year ago.

He was runner-up in Abu Dhabi, tied for fifth in Dubai, lost in the final of the Match Play Championship and then won the Honda Classic, making one clutch par save after another to hold off a late rally by Woods. McIlroy went to No. 1 by winning at PGA National, and he has been atop the world ranking since winning the PGA Championship.

How much longer he stays there depends on his game — and that of Woods, who is No. 2 and making up ground.

They are the featured players as the Florida swing gets under way Thursday in the Honda Classic, a tournament that has been rejuvenated in recent years with a couple of significant moves. One was the site of the tournament to PGA National, which has hosted a PGA Championship and a Ryder Cup and makes for good television with so much water in play over the closing holes.

The other was a vast improvement in the neighborhood. Woods moved to nearby Jupiter Island, while McIlroy, Lee Westwood and former Masters champion Charl Schwartzel are located at Old Palm just down the road. Keegan Bradley, Rickie Fowler, Dustin Johnson and others also have moved to south Florida.

It turned out to be the right recipe to get a good field, though Woods and McIlroy are at the top of the list, especially with the Masters getting closer.

Woods brings a little perspective to whether there is reason to doubt McIlroy.

The Match Play Championship is the most unpredictable event in golf, and Woods is a great example of that. He is the only three-time winner, yet he has yet to make it out of the second round since his last win. Woods played bogey-free on a course that still had traces of snow and was beaten by Charles Howell III, who played even better.

“Generally if you’re missing a cut, you’re probably not playing that well,” Woods said Wednesday after his pro-am round. “I actually played well, and only played one day. So I missed a few putts out there, but other than that, I really played well. And unfortunately, I ran into a guy who also played well — better than I did.”

McIlroy didn’t look sharp at all when he was eliminated by Shane Lowry. His weakness was iron play, leaving several shots out to the right. So was it his swing or his new equipment? The 23-year-old from Northern Ireland suggested a little of both.

“I guess it’s still an adjustment period,” he said. “It’s going to be a gradual thing. There’s obviously a bit of an overlap there and you have to just try and get your way into it the best you can. But as I’ve said the last few weeks, it’s more about how I’m swinging the club. That’s the real concern — not concern for me, but I would like to get back to where I was the middle of last year. That’s the real thing I’m working on.”

Even so, the switch to new equipment has been a factor.

McIlroy took a big break at the end of the 2011 season, nearly two months before starting a new year. But with an equipment change, he only took a few weeks off before getting to the practice range with his new clubs. Somewhere along the way, he says some bad habits got into his swing.

He said the golf ball was an easier adjustment than he expected. The driver was more difficult, though McIlroy is confident he has that dialed in.

Now it’s a matter of taking it to the golf course.

He is playing three times before he gets to the Masters — PGA National and Doral in back-to-back weeks, and then a two-week break before he plays the Houston Open.

Whether the Florida swing starts with the Honda Classic or Doral, as it once did, the feel of that warm, tropical breeze, palm trees, white bunkers and blue water hazards signal the first step toward the first major of the year. Only 34 players in the 144-man field are currently in the Masters.

The Honda Classic has five of the top 10 players in the world, including Westwood, Louis Oosthuizen and Justin Rose.

Not all the focus is on the road to the Masters. A divisive issue hanging over golf is the proposed rule that would ban anchored strokes used with long putters. The PGA Tour said last week it was opposed to the plan. Woods was among those who said the club should be swung freely, without being anchored to the body, and he stood by that.

What he doesn’t know is whether the governing bodies will go ahead with the rule, and how the PGA Tour responds.

“Hopefully, we don’t have to bifurcate or adapt a local rule like we sometimes out here on tour with stones and bunkers and things of that nature,” Woods said. “Hopefully, we won’t have to do that with our putter.”

He said he understood PGA Tour commissioner Tim Finchem’s position to oppose the ban, “but I still feel that all 14 clubs should be swung.”