A polynomial based far-field expansion for treecode algorithm

Do you believe that your computers do things so fast? You probably say yes. However, it depends on what fields we use computers in. Let me take an example of physics. In physics, they have tremendous data for research work, such as particle-particle interactions, like stars in a galaxy with different “gravity”. When they do computational modelling, using those data in a naïve way, it consumes a large portion of computer processing time and memory, which we call “expensive” method. “How can we process them in a clever way?” One of the common operation is matrix-vector multiplication, which most students learn from a linear algebra course. My research uses Fast treecode algorithms as a powerful tool to increase the speed of matrix-vector multiplications for some matrices that have special structure and are commonly used in physics and statistics. Treecode algorithms work by grouping particles into clusters whose effect on other, far-away particles can be rapidly approximated by using far-field expansion. In this project, we focus on the polynomial far-field expansion for the treecode algorithm, which has several potential advantages over the commonly used Taylor approximation. In other word, we want to make treecode algorithm more efficient and reliabl