scholarly journals Recovering exponential accuracy from collocation point values of smooth functions with end-point singularities

2014 ◽  
Vol 265 ◽  
pp. 83-95 ◽  
Author(s):  
Zheng Chen ◽  
Chi-Wang Shu
Keyword(s):  
Collocation Point ◽  
Smooth Functions ◽  
Exponential Accuracy ◽  
End Point

Filters, mollifiers and the computation of the Gibbs phenomenon

Acta Numerica ◽  
2007 ◽  
Vol 16 ◽  
pp. 305-378 ◽  
Author(s):  
Eitan Tadmor
Keyword(s):  
Physical Space ◽  
Gibbs Phenomenon ◽  
Delta Function ◽  
High Accuracy ◽  
Piecewise Smooth ◽  
Spectral Information ◽  
Smooth Functions ◽  
Exponential Accuracy ◽  
Local Loss ◽  
Edge Detectors

We are concerned here with processing discontinuous functions from their spectral information. We focus on two main aspects of processing such piecewise smooth data: detecting the edges of a piecewise smooth f, namely, the location and amplitudes of its discontinuities; and recovering with high accuracy the underlying function in between those edges. If f is a smooth function, say analytic, then classical Fourier projections recover f with exponential accuracy. However, if f contains one or more discontinuities, its global Fourier projections produce spurious Gibbs oscillations which spread throughout the smooth regions, enforcing local loss of resolution and global loss of accuracy. Our aim in the computation of the Gibbs phenomenon is to detect edges and to reconstruct piecewise smooth functions, while regaining the high accuracy encoded in the spectral data.To detect edges, we utilize a general family of edge detectors based on concentration kernels. Each kernel forms an approximate derivative of the delta function, which detects edges by separation of scales. We show how such kernels can be adapted to detect edges with one- and two-dimensional discrete data, with noisy data, and with incomplete spectral information. The main feature is concentration kernels which enable us to convert global spectral moments into local information in physical space. To reconstruct f with high accuracy we discuss novel families of mollifiers and filters. The main feature here is making these mollifiers and filters adapted to the local region of smoothness while increasing their accuracy together with the dimension of the data. These mollifiers and filters form approximate delta functions which are properly parametrized to recover f with (root-) exponential accuracy.

End Point

2020 ◽  
Author(s):  
Keyword(s):  
End Point

Settler Colonialism and the Revolutionary War

2019 ◽  
Vol 41 (4) ◽  
pp. 7-35
Author(s):  
Andrea Lynn Smith
Keyword(s):  
New York ◽  
Settler Colonialism ◽  
Revolutionary War ◽  
The State ◽  
The Public ◽  
150Th Anniversary ◽  
End Point ◽  
Indian Land ◽  
Indian Relations ◽  
Major General

The centerpiece of New York State’s 150th anniversary of the Sullivan Expedition of 1779 was a pageant, the “Pageant of Decision.” Major General John Sullivan’s Revolutionary War expedition was designed to eliminate the threat posed by Iroquois allied with the British. It was a genocidal operation that involved the destruction of over forty Indian villages. This article explores the motivations and tactics of state officials as they endeavored to engage the public in this past in pageant form. The pageant was widely popular, and served the state in fixing the expedition as the end point in settler-Indian relations in New York, removing from view decades of expropriations of Indian land that occurred well after Sullivan’s troops left.

APLIKASI CITRA LANDSAT DALAM ANALISA PERUBAHAN GARIS PANTAI (Studi Kasus di Pesisir Sayung, Kabupaten Demak, Jawa Tengah)

2019 ◽  
Vol 3 ◽  
pp. 919
Author(s):  
Khairul Umami ◽  
Syawaludin A. Harahap ◽  
Mega Laksmini Syamsudin ◽  
Sunarto Sunarto
Keyword(s):  
End Point ◽  
Digital Shoreline Analysis System ◽  
Landsat 7 ◽  
Analysis System ◽  
End Point Rate

Pantai merupakan daerah yang sangat dinamis untuk berubah seiring bertambahnya waktu. Salah satu perubahan yang terjadi di daerah pantai yaitu perubahan pada garis pantai. Tujuan penelitian ini yaitu untuk mengetahui tingkat perubahan garis pantai di pesisir Kecamatan Sayung, Kabupaten Demak dari hasil overlay citra satelit Landsat. Penelitian ini diharapkan dapat berguna sebagai rujukan penelitian selanjutnya, serta sebagai informasi untuk instansi-instansi terkait dan pemerintah agar dapat memperhatikan kondisi keseimbangan fisik pantai di Pesisir Sayung. Penelitian ini menggunakan data yang bersumber dari citra Landsat 7 dan 8 dalam kurun waktu 10 tahun dari tahun 2006 sampai 2016. Metode yang digunakan yaitu metode deskriptif dengan menjelaskan masalah yang terjadi pada lokasi penelitian dengan pendekatan pemodelan dan sistematis. Metode analisis perubahan garis pantai dilakukan dalam program Digital Shoreline Analysis System (DSAS) dengan pendekatan statistik End Point Rate (EPR) dan Net Shorline Movement (NSM). Hasil penelitian menunjukkan bahwa perubahan garis pantai di pesisir Sayung didominasi dengan kejadian abrasi yang sangat tinggi dengan luasan abrasi bernilai 116,48 hektar. Abrasi maksimum terjadi di Desa Timbulsloko, Abrasi minimum terjadi di Desa Sriwulan, Akresi maksimum terjadi di Desa Sriwulan, dan Akresi minimum terjadi di Desa Bedono.

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