Hasil Pencarian  ::  Simpan CSV :: Kembali

"The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control.In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject."

"The material covered includes Householder and Givens orthogonal transformations, the QR and SVD decompositions, equality constraints, solutions in nonnegative variables, banded problems, and updating methods for sequential estimation. Both the theory and practical algorithms are included. The easily understood explanations and the appendix providing a review of basic linear algebra make the book accessible for the non-specialist."

"This self-contained textbook presents matrix analysis in the context of numerical computation with numerical conditioning of problems and numerical stability of algorithms at the forefront. Using a unique combination of numerical insight and mathematical rigor, it advances readers understanding of two phenomena: sensitivity of linear systems and least squares problems, and numerical stability of algorithms."

"As mentioned before in the submitted proposal, the aim of this investigation is to study the wide angle reflection characteristic which has both advantage and disadvantage. The advantage we could obtain from such reflection angle is the stronger reflections (i.e S/N ratio) compared to the narrower angle reflections. This strong reflection makes the horizon identification becomes easier and its amplitudes might be used to study the rock properties using inversion technique. Its disadvantage comes from the fact that wide angle reflection involves what co-called chase distortion that affects the travel-time picking and also the amplitude measurement.Some workers have studied the phase distortion effect and proposed some methods to overcome the problem. Choy and Richards [2] who studied seismograms produced by a caustic region found the similarities between event in the original seismograms and the Hilbert transformed seismograms. They observed that, for example, an sS-wave is a Hilbert transform pair of an SS-wave, which suggested a 90° phase distortion. To tackle the problem of obscure travel-time, they applied the matched filter to the distorted signal after Hilbert transforming the reference signal. This method, however, is limited to 913° phase distortion only.The matched filter is a simple and straightforward method to estimate the amplitude ratio and differential travel-time of two different signals. However, it works well only when both signals have similar waveforms. When the phase distortion occurs, i.e. the original waveform is distorted, the matched filter fails to obtain an optimum amplitude and travel-time estimations. Pointer and Neuberg [8] introduced an iterative matched filter for analysing the effect of a phase distortion. First, the reference signal is phase distorted and used to find the amplitude ratio and travel-time by matched filter. The procedure is repeated ti changing the phase with a particular increment until they obtain the best cross-correlation value automatically revealing the amplitude ratio, the differential travel-time, and the phase distortion. However, the method is sensitive to the choice of the phase increment and in some cases it."