By Charles Van Loan
The main finished remedy of FFTs so far. Van personal loan captures the interaction among arithmetic and the layout of powerful numerical algorithms--a severe connection as extra complex machines turn into on hand. A stylized Matlab notation, that's everyday to these engaged in high-performance computing, is used. the quick Fourier rework (FFT) kinfolk of algorithms has revolutionized many parts of medical computation. The FFT is among the most generally used algorithms in technological know-how and engineering, with purposes in virtually each self-discipline. This quantity is vital for pros drawn to linear algebra in addition to these operating with numerical equipment. The FFT is additionally an outstanding car for instructing key points of medical computing.
Read or Download Computational Frameworks for the Fast Fourier Transform (Frontiers in Applied Mathematics) PDF
Best computational mathematicsematics books
This e-book constitutes the refereed complaints of the eighth Dortmund Fuzzy Days, held in Dortmund, Germany, 2004. The Fuzzy-Days convention has verified itself as a global discussion board for the dialogue of latest leads to the sphere of Computational Intelligence. the entire papers needed to endure a radical overview ensuring an exceptional caliber of the programme.
The sector of Socially clever brokers (SIA) is a quick starting to be and more and more vital quarter that contains hugely lively learn actions and strongly interdisciplinary techniques. Socially clever brokers, edited through Kerstin Dautenhahn, Alan Bond, Lola Canamero and Bruce Edmonds, emerged from the AAAI Symposium "Socially clever brokers -- The Human within the Loop".
This booklet provides an easy-to-read dialogue of area decomposition algorithms, their implementation and research. The authors conscientiously clarify the connection among area decomposition and multigrid equipment at an straightforward point, and so they talk about the implementation of area decomposition equipment on vastly parallel supercomputers.
Additional info for Computational Frameworks for the Fast Fourier Transform (Frontiers in Applied Mathematics)
1 An In-Place Formulation Many FFT procedures require storage beyond what is required for the z-vector. A notable exception to this is the following version of the Cooley-Tukey algorithm. 6. 5, it does not require a vector workspace for execution. 9) to obviate the need for a weight vector workspace. 1). These strategies are of interest in limited storage situations. An FFT algorithm that does not require a vector workspace is called an in-place FFT. 2) with weight precomputation. 2 with Fnx: If x 6 C" and n = 2', then the following algorithm overwrites x The fact that this algorithm requires a workspace devalues its importance, for as we said above, a key attribute of the Cooley-Tukey framework is that it permits the inplace computation of Fnx.
Chu (1988). D. Thesis, Center for Applied Mathematics, Cornell University, Ithaca, NY. J. Oliver (1975). "Stable Methods for Evaluating the Points cos(tV/n)," J. Inst. Maths. Applic. 16, 247-257. Once the properties of the computed weights are known, then it is possible to address the accuracy of the FFT itself. The following papers take a statistical approach to the problem: 36 CHAPTER 1. THE RADix-2 FRAMEWORKS R. Alt (1978). "Error Propagation in Fourier Transform*," Math. Comp. Sim*/. 20, 37-43.
Abramovici (1975). "The Accuracy of Finite Fourier Transforms," J. Comput. Pkya. 17, 446-449. M. Arioli, H. Munthe-Kaas, and L. Valdettaro (1991). "Componentwise Error Analysis for FFT's with Applications to Fast Helmoltz Solvers," CERFACS Report TR/IT/PA/91/55, Toulouse, France. T. Kaneko and B. Liu (1970). "Accumulation of Roundoff Error in Fast Fourier Transforms," J. Aaaoca. Comput. Much. 17, 637-54 . U. Ramos (1971). "Roundoff Error Analysis of the Fast Fourier Transform," Math. Comp. 25, 757-768.