Nuclear Physics Seminar
Wavelet methods in Few-Body Scattering
Wayne Polyzou (U. Iowa)
Wavelets are basis functions that are known for their ability to
efficiently represent functions. JPEG files, that are used to
compress digital photographs, contain the coefficients of wavelet basis
functions. The FBI uses wavelets to store and compare fingerprints
efficiently. The ability to reduce a square array of pixels to an
equivalent sparse array suggests that the same method could be used to
approximate the dense kernels that appear in momentum-space scattering
integral equations by sparse matrices. Because the basis functions
are generated by solving a linear renormalization group equation, they
have structure on all scales. This leads to the problem that
conventional numerical methods no longer work efficiently. I discuss
how the renormalization group equation can be used to overcome these
difficulties and discuss some possible applications of wavelet methods
in nuclear physics.
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