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"The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra. The topics include polynomial interpolation, Bernstein polynomials and the Weierstrass theorem, best approximations in the general setting of normed linear spaces and inner product spaces, best uniform polynomial approximation, orthogonal polynomials, Newton-Cotes , Gauss and Clenshaw-Curtis quadrature, the Euler-Maclaurin formula, approximation of periodic functions, the uniform convergence of Fourier series, spline approximation,with an extensive treatment of local spline interpolation,and its application in quadrature. Exercises are provided at the end of each chapter."

"Contains the proceedings that were prepared in connection with the international conference Approximation Theory XIII, which was held March 7-10, 2010 in San Antonio, Texas. This book includes many relevant topics in approximation theory, such as abstract approximation, approximation with constraints, and interpolation and smoothing."

"This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. In addition, some facts concerning trigonometric approximation that are necessary for motivation and comparisons are included. The selection of papers that are referenced and discussed document some trends in polynomial approximation from the 1950s to the present day."

"These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7–10, 2010 in San Antonio, Texas. The conference was the thirteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 144 participants. Previous conferences in the series were held in Austin, Texas (1973, 1976, 1980, 1992), College Station, Texas (1983, 1986, 1989, 1995), Nashville, Tennessee (1998), St. Louis, Missouri (2001), Gatlinburg, Tennessee (2004), and San Antonio, Texas (2007).Along with the many plenary speakers, the contributors to this proceedings provided inspiring talks and set a high standard of exposition in their descriptions of new directions for research. Many relevant topics in approximation theory are included in this book, such as abstract approximation, approximation with constraints, interpolation and smoothing, wavelets and frames, shearlets, orthogonal polynomials, univariate and multivariate splines, and complex approximation."

"Telah dilakukan inversi Elastic Impedance dan Dekomposisi Spektral pada lapangan Penobscot, untuk mengidentifikasi reservoir pada lapisan tipis. Perkembangan atribut seismik dewasa ini sangat membantu dalam menunjukkan indikasi adanya hidrokarbon pada reservoir. Atribut Dekomposisi Spektral yang didasari dari hasil komputasi CWT diharapkan dapat menjadi atribut yang berguna untuk mendeteksi adanya indikasi keberadaan hidrokarbon pada lapisan tipis. Untuk mendukung hasil metode CWT, akan dikombinasikan dengan hasil metode inversi untuk meyakinkan akan keberadaan hidrokarbon tersebut yang ditandai dengan nilai Elastic Impedance (EI) yang relatif rendah dengan sekitarnya.Dari hasil studi ini frekuensi dominan terlihat pada frekuensi 25 Hz, sedangkan pada frekuensi 10 Hz (frekuensi rendah) dan 30 Hz (frekuensi tinggi) anomali bright spot tidak terlihat di beberapa daerah prospek. Hal ini didukung dengan hasil inversi yang menunjukkan nilai EI yang rendah yaitu berkisar 13000 - 13750 ((ft/s) *(gr/cc)), 2370 - 2511((ft/s) *(gr/cc)), dan 600 - 620((ft/s) *(gr/cc)). Kombinasi metode dekomposisi spektral berbasis CWT dengan metode inversi seismik (EI) mengindikasikan adanya akumulasi gas pada beberapa daerah prospek.

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The Elastic Impedance inversion and the Spectral Decomposition process at the Penobscot field has been carried out, in order to identify the reservoir on a thin layer. The development of seismic attributes these days are very helpful in indicating any presence of Hydrocarbons in the reservoir. The Spectral Decomposition attribute, that based on the results of CWT computation is expected to become applicable in detecting and indicating any presence of Hydrocarbons in a thin layer. In order to support the results of CWT method, it will be combined with the one from the Inversion method, to assure the existence of such hydrocarbons which are characterized by the Elastic Impedance (EI) value that should be relatively low with its surroundings.

From the results of this study, the dominant frequency appears at 25 Hz, while in the frequency of 10 Hz (low frequency) and 30 Hz (high frequency), the bright spot anomaly has not been seen in some prospect areas. This result is supported by the inversion results that shows rather low EI values, ranged from 13000 to 13750 ((ft / s) * (g / cc)), from 2370 to 2511 ((ft / s) * (g / cc)), and from 600 to 620 ((ft / s) * (g / cc)). The combination of CWTbased spectral decomposition method with the seismic inversion methods (EI) indicates that there are an accumulation of gas in a some prospect areas."

"Lapangan Salemba dan Depok adalah lapangan gas yang berada di daerah Selat Madura. Pada dua sumur eksplorasi telah ditemukan akumulasi hidrokarbon gas pada Formasi Lidah yang berumur Plio-Pleistocene. Formasi Lidah didaerah studi ini diinterpretasikan sebagai sistem pengendapan channel. Permasalahan yang muncul dalam menganalisa data seismik untuk mengetahui geometri dari channel sendiri adalah adanya lapisan tipis yang tidak terdeteksi dan batas kontinuitas pelapisan yang kurang jelas. Oleh karena itu, diperlukan metode yang lebih baik untuk analisa data seismik agar masalah tersebut dapat diatasi.Dalam tesis ini, analisa data seismik metode dekomposisi spektral dengan algoritma Continuous Wavelet Transform (CWT) digunakan karena hasilnya dapat memberikan gambaran yang lebih baik dalam penyebaran ketebalan dan diskontinuitas geologi. Selain itu juga digunakan metode inversi seismik untuk mengetahui penyebaran impedansi akustik yang merupakan sifat fisis batuan.Hasil studi ini menunjukkan bahwa metode dekomposisi spektral dan inversi seismik telah berhasil membantu dalam mendeliniasi geometri channel Formasi Lidah. Penampang dekomposisi spektral merepresentasikan ketebalan dan diskontuniuitas geologi dari reservoir batupasir Formasi Lidah. Distribusi frekuensi pada reservoir direpresentasikan pada nilai frekuensi 10, 20, dan 30 Hz. Pada inversi seismik, penampang impedansi akustik merepresentasikan litologi bawah permukaan. Distribusi impedansi akustik pada reservoir mempunyai nilai rata-rata 15000 - 19700 ((ft/s)*(g/cc)), sedangkan pada non-reservoir mempunyai nilai impedansi akustik lebih dari 19700 ((ft/s)*(g/cc)).

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Salemba and Depok fields are a gas field which located in the Madura Strait. Two exploration wells have been discovered hydrocarbons accumulation of gas in the Lidah Formation aged Plio-Pleistocene. Lidah Formation in the study area was interpreted as channel depositional environment. The problem that then arises in analyzing seismic data to predict the channel geometry is undetected thin layer and unclear reservoir continuity. Therefore, the better method to analyze the seismic data is needed to solve the problem.

In this thesis, seismic data analysis spectral decomposition method with Continuous Wavelet Transform (CWT) is used because the results can provide a better map of the thickness distribution and geological discontinuities. This thesis is also used seismic inversion method to know the acoustic impedance distribution as the physical properties of rocks.

The result of this study shows that the spectral decomposition method and seismic inversion has helped to delineate the channel geometry of Lidah Formation. The section of spectral decomposition represents thickness and geological discontinuity in Lidah Formation. Frequency distribution in the reservoir has an average of 10, 20, and 30 Hz. In the seismic inversion, the section of acoustic impedance represents the subsurface lithology. Acoustic impedance distribution in the reservoir has an average of 15,000 - 19,700 ((ft/s)*(g/cc)), whereas in nonreservoir having an acoustic impedance more than 19,700 ((ft/s)*(g/cc))."

"Data approximation by low-complexity models details the theory, algorithms, and applications of structured low-rank approximation. Efficient local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. Much of the text is devoted to describing the applications of the theory including, system and control theory, signal processing, computer algebra for approximate factorization and common divisor computation, computer vision for image deblurring and segmentation, machine learning for information retrieval and clustering, bioinformatics for microarray data analysis, chemometrics for multivariate calibration, and psychometrics for factor analysis."