Rounding error in least squares approximation with applications in financial mathematics
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Currently, there are many numerical techniques which can be used to estimate Least-Squares polynomial approximations to model interest rates. Four of these techniques are the Least-Squares approximation, the QR Decomposition approach to solving the Least-Squares problem, the Gram-Schmidt Orthogonalization Process approach to solving the Least-Squares problem and the Discrete Legendre Polynomial approach to solving the Least-Squares problem. Each of these four approaches is studied herein. A comparative study is used throughout to determine which has the least rounding error. Chapter II breaks down each of these four methods into their many parts and explains them with a mathematical approach. This chapter abstractly presents the steps that each computer program is going to take. In essence, chapter two is a study of the many components of each of the methods. The third chapter starts our analysis of these procedures. Two reference examples are given and a preliminary hypothesis is made. In the fourth chapter, some data on US Treasury STRIPS is looked at. both computationally and graphically. The final chapter presents a conclusion of all of these results.