A.G. Buckley, J-.L. Goffin's Algorithms for Constrained Minimization of Smooth Nonlinear PDF

By A.G. Buckley, J-.L. Goffin

ISBN-10: 3642008127

ISBN-13: 9783642008122

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7] have come to pass. Novel applications to digital logic design, pattern recognition, data compression, magnetic resonance imaging, neuroscience and quantum computing are emerging. Similarly, signal spreading using Hadamard matrices, foreshadowed in [142], is well known in digital and satellite communications and is commonplace globally in CDMA mobile phones, but is an emergent technique in automated learning, ultrasonics, optical communication and information hiding. We will describe these applications from the perspective of digital signal processing.

2126]; for a picture, see [237, Fig. 7]). Golay codes were similarly applied in the Voyager missions, returning clear colour pictures of Jupiter and Saturn until 1981 (see [263, Ch. 25]). The Reed-Muller codes lost their prominence in the space program with the adoption of convolutional codes and sequential decoders. They do not perform as well as long BCH and Reed-Solomon codes, but they have the benefit of an extremely fast maximum likelihood decoding algorithm. Wicker [321] points out that there is renewed interest in using Reed-Muller codes in optical communications because of this.

17 Let G be a group of order v, written multiplicatively, with a fixed ordering {g1 , g2 , . . , gv }. A matrix with entries from a set S is group developed over G (briefly: G-developed) if the rows and columns of the matrix are indexed by the elements of G and there is a map φ : G → S such that the entry in position (i, j) is φ(gi gj ), for 1 ≤ i, j ≤ v. We denote such a matrix by [φ(gi gj )]1≤i,j≤v . A matrix is group-invariant (or G-invariant) if the entry in position (i, j) is φ(gi gj−1 ), for 1 ≤ i, j ≤ v.

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Algorithms for Constrained Minimization of Smooth Nonlinear Functions by A.G. Buckley, J-.L. Goffin


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