本文介绍了斐波那契数列的一些算法思路，对递归算法、自底向上、比内公式等算法的时间复杂度进行了分 析，给出了利用矩阵乘法升维计算降低时间复杂度的方法，对比测试了各算法实现在不同计算量下的执行时间。针对数据溢 出，将long数据类型改进为BigInteger的数据类型,给出了大数计算下的执行时间对比。

This paper introduces some algorithms of Fibonacci sequence calculation, analyzes the time complexity of recursive, bottom-up and Binet formula algorithms, gives a method to reduce the time complexity by using two dimension matrix multiplication, and compares the execution time of different amount of calculation among these algorithms. It modifies the long data type to BigInteger data type to resolve the data overflow problem, and compares different algorithms’execution time for large number calculation.