Showing papers on "Maxima and minima published in 1974"
Book•
01 Jan 1974
TL;DR: In this article, the authors provide a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasize their relationships, and provide a set of methods of quantifying the relationship between these eigenvectors.
Abstract: Provides a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasizes their relationships.
288 citations
TL;DR: In this article, a method of solving problems on extrema with constraints of the equality type is considered, at each step of which a Lagrange function modified by the addition of a penalty function is minimized.
Abstract: WE consider a method of solving problems on extrema with constraints of the equality type, at each step of which a Lagrange function modified by the addition of a penalty function is minimized. It is proved that this method converges locally at the rate of a geometrical progression whose denominator is smaller, the greater the penalty coefficient.
57 citations
TL;DR: An algorithm that uses the difference between the magnitude of the convex hull of the loudness function and the function itself as a measure of significance and recursively subsegments to the total signal until a given threshold of difference is nowhere exceeded is used.
Abstract: An algorithm has been designed to detect boundaries between syllabic segments of the speech signal, segments that contain but one peak or syllabic phoneme. A loudness function is defined, roughly corresponding to the short‐time signal energy, and this function exhibits alternating sequence of points of relatively major maxima and minima. No absolute energy criteria appear adequate to decide whether a given maximum in the function is in fact a syllabic peak. However, minima can be characterized as significant with reference to the magnitudes of neighboring maxima. The algorithm uses the difference between the magnitude of the convex hull of the loudness function and the function itself as a measure of significance and recursively subsegments to the total signal until a given threshold of difference is nowhere exceeded. The algorithm is used as the first stage of a sequential procedure for segmentation and phonetic labeling of speech for recognition applications. [Research supported by the Advanced Research Projects Agency, Department of Defense].
9 citations
TL;DR: This paper pointed out some rather elementary mathematical errors perpetuated in textbooks and pointed out that these errors are often overlooked by the authors of the textbooks, and pointed them out in the book.
8 citations
8 citations
TL;DR: Probability distributions for the heights of maxima and minima in fluctuating nuclear cross sections have been obtained from synthetic excitation functions as mentioned in this paper, and these distributions can be used to determine the extent to which experimentally ob
Abstract: Probability distributions for the heights of maxima and minima in fluctuating nuclear cross sections have been obtained from synthetic excitation functions. It is shown how these distributions can be used to determine the extent to which experimentally ob
2 citations