TOKYO, Oct 26 (Reuters) - Japan’s Nikkei share average rallied strongly on Tuesday amid earnings optimism, and following gains on Wall Street overnight that took the Dow and S&P 500 to record highs. The Nikkei added 1.8% to 29,100.57 as of the midday break, with heavily weighted names like Uniqlo-owner Fast Retailing jumping 4.2% and SoftBank Group rising 2.2%. The broader Topix advanced 1.2% to 2,019.30, with all 33 sectors posting gains, led by a 2.6% rally in iron and steel companies. U.S. e-mini futures pointed to a 0.3% rise at the re-open for the S&P 500, and an index of Asia-Pacific stocks outside Japan also edged higher, further supporting investor sentiment. A large proportion of S&P 500 companies are due to report results this week, including technology heavyweights Apple, Amazon, Microsoft, and Google-operator Alphabet, which have been the drivers of the Wall Street rally this year. Sony Group rose 2.4% to the highest since 2000 ahead of earnings results on Thursday. Motor-maker Nidec added 0.4% before reporting financial results later Tuesday. “Before earnings season gets into full swing, the market is focused the psychologically important 29,000 level, and investors may want to take a wait-and-see attitude there,” said a market participant at a domestic securities firm. (Reporting by Tokyo markets team; editing by Uttaresh.V) Our Standards: The Thomson Reuters Trust Principles.