关键词：误差分析；兰索斯法；有限精度
摘 要：The s-step Lanczos method is an attractive alternative to the classical Lanczos method as it enables an O(s) reduction in data movement over a xed number of iterations. This can signi cantly improve performance on modern computers. In order for s-step methods to be widely adopted, it is important to better understand their error properties. Although the s-step Lanczos method is equivalent to the classical Lanczos method in exact arithmetic, empirical observations demonstrate that it can behave quite di erently in nite precision. In the s-step Lanczos method, the computed Lanczos vectors can lose orthogonality at a much quicker rate than the classical method, a property which seems to worsen with increasing s.