Stocks rebound after a rough week.

U.S. stocks rebounded on Tuesday, the first trading day after a tumultuous week on Wall Street, its worst since early in the pandemic and the official start of a bear market.

The S&P 500 opened up about 1.6 percent, regaining some of the ground lost last week. The benchmark index is down about 24 percent from its January peak.

Analysts at Goldman Sachs published a report on Tuesday that looked at bear markets back to the 19th century, and concluded that the current downturn is most akin to other “cyclical” bear markets, in which “inflation and interest rates are rising and markets are pricing the risk of a recession.” These bear markets recorded an average decline of about 30 percent from their peak over the course of two years, and took about five years to recover to its starting point.

• Kellogg, the packaged food manufacturing giant, announced on Tuesday that it planned to split into three companies that would focus on snacks, cereal and plant-based food. The newly independent companies each have “significant standalone potential,” Steve Cahillane, Kellogg’s chief executive, said in a statement, and the split would give them “enhanced focus” on their specific markets. The company’s stock rose 5 percent in early trading.

• Twitter’s board wrote to shareholders on Tuesday, unanimously recommending that investors vote to approve Elon Musk’s $44 billion acquisition offer. Speaking virtually at a conference hosted by Bloomberg earlier in the day, Mr. Musk said that there were “a few unresolved matters” in his negotiations with Twitter, as he continues to push for information about fake accounts on the platform, which some see as a pretext for ending or renegotiating the deal. Twitter’s share price rose 1.2 percent, but remains far below the price offered by Mr. Musk, implying doubts that the deal will be done on the current terms.

• In Europe, the Stoxx 600 index was up 0.5 percent and the Hang Seng in Hong Kong and the Nikkei 225 in Tokyo both gained nearly 2 percent.

• Bitcoin rose to about $21,200 after falling below $20,000 this weekend, for the first time since December 2020.