Numerical stability of fast trigonometric and orthogonal wavelet transforms
نویسندگان
چکیده
Fast trigonometric transforms and periodic orthogonal wavelet transforms are essential tools for numerous practical applications. It is very important that fast algorithms work stable in a floating point arithmetic. This survey paper presents recent results on the worst case analysis of roundoff errors occurring in floating point computation of fast Fourier transforms, fast cosine transforms, and periodic orthogonal wavelet transforms. All these algorithms realize matrix-vector products with unitary matrices. The results are mainly based on a factorization of a unitary matrix into a product of sparse, almost unitary matrices. It is shown that under certain conditions fast trigonometric and periodic orthogonal wavelet transforms can be remarkably stable. §
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