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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 1994 • Question 8

Question

Math 6610 • Analysis of Numerical Methods I Fall 1994 • Question 8

a) Give an identity that is the basis of one stage of the Fast Fourier Transform algorithm applied to a vector of length \(2^J\). Explain the approximate operation count for the complete algorithm.

b) Describe the application of the FFT to the solution of the heat equation with periodic boundary conditions, and how this may be viewed as performing a fast convolution.

Raw LaTeX

\textbf{a)} Give an identity that is the basis of one stage of the Fast Fourier
Transform algorithm applied to a vector of length \(2^J\). Explain the approximate
operation count for the complete algorithm.

\textbf{b)} Describe the application of the FFT to the solution of the heat
equation with periodic boundary conditions, and how this may be viewed as
performing a fast convolution.

Topic Tags

Finite Difference Boundary Value Problems Linear Programming and Optimization Zero-Stability and Root Conditions