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"As this monograph shows, the purpose of cardinal spline interpolation is to bridge the gap between the linear spline and the cardinal series. The author explains cardinal spline functions, the basic properties of B-splines, including B- splines with equidistant knots and cardinal splines represented in terms of B-splines, and exponential Euler splines, leading to the most important case and central problem of the book-- cardinal spline interpolation, with main results, proofs, and some applications. Other topics discussed include cardinal Hermite interpolation, semi-cardinal interpolation, finite spline interpolation problems, extremum and limit properties, equidistant spline interpolation applied to approximations of Fourier transforms, and the smoothing of histograms."

"The UN Volume (Bogue, Arriaga and Anderton, l993)on population methodology has elaborated different methods forinterpolation of population data. There were two methods ininterpolating empirical data frequently discussed, that are mid-point method and cumulation-differencing method In some casesmid-point method was not recommended and cumulation-differencing method was recommended only on the basis of limiteddata. This study tries to explore other methods in manipulatingpopulation data for different nature of data. The paper when atone instance, finds that the method which was not recommended bythe said volume was acceptable using different nature of data. Inother case, the method which was recommended in the volume was_,round more sound in respect of other kind of data In addition,some new types of data have also been tried and appropriateinterpolation formulae were recommended."

"Penelitian ini membahas tentang penggabungan data seismik high density dan low density shot menggunakan metode interpolasi 5D Matching Pursuit Fourier Interpolation (MPFI). Tujuan utama dari penelitian ini adalah untuk menghasilkan dataset seismik dengan kualitas yang lebih tinggi melalui penggabungan kedua set data yang memiliki densitas yang berbeda dan mengurangi efek leakage dan aliasing yang ada pada data seismik yang terakuisisi secara irregular. Metode MPFI dilakukan dengan menggabungkan metode Anti Leakage Fourier Transform (ALFT) dan Anti Aliasing. Metode ini melibatkan iterasi dan pemberian pembobotan (prior) pada proses interpolasi. Hasil penelitian menunjukkan bahwa metode interpolasi 5D MPFI berhasil menghasilkan dataset seismik gabungan yang memiliki resolusi spasial lebih tinggi daripada kedua set data asli. Hal ini ditunjukkan oleh tingginya signal to noise (S/N ratio), kemenerusan yang lebih koheren, patahan yang lebih terdefinisi, serta amplitudo yang lebih seimbang. Interpolasi juga berhasil mengisi celah antara data high density dan low density, serta melakukan regularisasi pada data yang terkena efek leakage dan aliasing. Selain itu, metode ini memperluas distribusi azimuth sehingga dapat digunakan untuk analisis kecepatan dalam berbagai arah, seperti AVAZ, VVAZ, dan Azimuthal PSDM. Selain menghasilkan dataset yang lebih baik, metode interpolasi ini juga memiliki keuntungan dalam hal penghematan biaya dibandingkan dengan melakukan akuisisi seismik ulang......This research studies merging high density and low density shot seismic datasets using the 5D Matching Pursuit Fourier Interpolation (MPFI) method. The main objective of this research is to achieve a higher quality seismic dataset by merging two datasets that have different densities and reducing the leakage and aliasing effects present in irregularly acquisition seismic data. The MPFI method is performed by combining the Anti Leakage Fourier Transform (ALFT) and Anti Aliasing methods. This method involves iteration and weighting (prior) in the interpolation process. The results show that the 5D MPFI interpolation method successfully produces a combined seismic dataset that has a higher spatial resolution than the two original datasets. This is indicated by the high signal to noise (S/N ratio), more coherent continuity, well defined faults, and more balanced amplitudes. The interpolation also effectively fills the gap between the high density and low density data, and regularizes the data affected by leakage and aliasing. In addition, this method extends the azimuth distribution so that it can be used for velocity analysis in multiple directions, such as AVAZ, VVAZ, and Azimuthal PSDM. In addition to producing better datasets, this interpolation method also has benefits in terms of cost savings compared to performing another seismic acquisition"

"This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.​"

"This book presents methods of mathematical modeling from two points of view. Splines provide a general approach while compartment models serve as examples for context related to modeling. The preconditions and characteristics of the developed mathematical models as well as the conditions surrounding data collection and model fit are taken into account. The substantial statements of this book are mathematically proven. The results are ready for application with examples and related program codes given.In this book, splines are algebraically developed such that the reader or user can easily understand and vary the numerical construction of the different kinds of spline functions. The classical compartment models of the pharmacokinetics are systematically analyzed and connected with lifetime distributions. As such, parameter estimation and model fit can be treated statistically with a varied minimum chi-square method. This method is applicable for single kinetics and also allows the calculation of average kinetics.--"