group

#### Authors' Class Standing

Austin Ogle, Junior Jacki Qi, Graduated Senior

#### Lead Presenter's Name

Austin Ogle

#### Faculty Mentor Name

Sirani M. Perera

#### Abstract

Modeling phenomenon of the interpolation problems can be seen in propagation of waves, weather conditions, real-time traffic patterns, signal processing, etc. There are different interpolation methods like polynomial interpolation, spline interpolation, rational interpolation, exponential interpolation, trigonometric interpolation, etc. In this situation, a fast *Bj* *rck-Pereyra-type algorithm *can be derived to solve this problem.

In this poster we will present the most general trigonometric interpolation problems to solve complex-Vandermonde system. We present a fast algorithm for solving a system where the coefficient-matrix is a complex Vandermonde matrix. This method is much more favorable than the Gaussian elimination, which ignores the structure of the Vandermonde Matrix.

*The new algorithm applies to a fairly general new class to solve trigonometric interpolation problems. We present numerical experiments while elaborating better forward error bound than the Gaussian elimination. Moreover, we analyze, compare, and contrast the connection of trigonometric interpolation problems to phase polynomials interpolation problems through complexity, forward error, and stability of algorithms. *

#### Did this research project receive funding support (Spark or Ignite Grants) from the Office of Undergraduate Research?

No

A Fast Bjo ̈rck-Pereyra-type Algorithm for Solving Complex-Vandermonde Systems

Modeling phenomenon of the interpolation problems can be seen in propagation of waves, weather conditions, real-time traffic patterns, signal processing, etc. There are different interpolation methods like polynomial interpolation, spline interpolation, rational interpolation, exponential interpolation, trigonometric interpolation, etc. In this situation, a fast *Bj* *rck-Pereyra-type algorithm *can be derived to solve this problem.

In this poster we will present the most general trigonometric interpolation problems to solve complex-Vandermonde system. We present a fast algorithm for solving a system where the coefficient-matrix is a complex Vandermonde matrix. This method is much more favorable than the Gaussian elimination, which ignores the structure of the Vandermonde Matrix.

*The new algorithm applies to a fairly general new class to solve trigonometric interpolation problems. We present numerical experiments while elaborating better forward error bound than the Gaussian elimination. Moreover, we analyze, compare, and contrast the connection of trigonometric interpolation problems to phase polynomials interpolation problems through complexity, forward error, and stability of algorithms. *