Nintendo released version 1.1.1 of The Legend of Zelda: Breath of the Wild for the Nintendo Switch to "make for a more pleasant gaming experience." That's not a particularly descriptive patch note, but early impressions show that noticeable frame rate issues have been mitigated, if not totally resolved.
We noted in our hands-on with the Switch that, although we didn't measure Breath of the Wild's frame rate, dips below its target 30fps were easily seen with the naked eye. To avoid story and gameplay spoilers, we'll say only that the frame rate tended to drop most often in specific locations or when combat involved more than one enemy. It certainly didn't ruin our experience with the game, but it was definitely notable, and sometimes distracting.
Revisiting some of those locations or entering combat with patch 1.1.1 installed showed that at least some of the issues have been addressed. We didn't spot any drops in some places, and in others, we noticed fewer stutters than we did before. Note that this is with the Switch in TV mode; playing Breath of the Wild in handheld mode resulted in very few drops even before this update, perhaps because it renders at 720p instead of the TV mode's 900p.
These problems didn't take us by surprise. Breath of the Wild started development as a Wii U game, and as the directors' presentation at GDC 2017 alluded to with a mock email instructing them to prepare the game for the Switch's launch, the dev team didn't have much time to optimize for the new hardware. (Nintendo's been surprisingly open about Breath of the Wild's development--it even published a multi-part documentary about the process.)
You can install version 1.1.1 of Breath of the Wild for Nintendo Switch by launching the game from the console's menu, which will automatically start the download process, or by pressing the - or + buttons on the console's controllers, selecting the Software Update option, and choosing Via the Internet. The patch is free, so you don't have to worry about buying the Expansion Pass, which offers access to current and upcoming downloadable content.
Nintendo also released this patch for the Wii U version of Breath of the Wild, but we haven't been able to test that version of the game, so we can't speak to its performance before or after the update. The performance update on both consoles highlights Nintendo's commitment both to its previous console--Breath of the Wild was the company's last game for the Wii U--and to making sure the Switch's launch problems don't go unaddressed.