Acceleration of software execution time for operations involving sequences or matrices

The article describes three methods for lowering program runtime that are solutions to computer science Olympiad problems involving sequences or matrices. The first method relies on the representation of some sequences as matrices, after which the program for calculating the sequence's members will have asymptotics equivalent to the exponentiation algorithm's time complexity and be O(log (n)). The second strategy is to improve the existing code in order to significantly shorten program runtime. For scientists who create code for scientific inquiries and deal with matrix multiplication operations, understanding this approach is crucial. The author's challenge is presented and solved using the third strategy, which is based on minimizing temporal complexity by looking for regularities.