Browsing by Author "Blais, J. A. Rod"
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Item Open Access Discrete Spherical Harmonic Transforms for Equiangular Grids of Spatial and Spectral Data(Versita, 2010-12) Blais, J. A. RodItem Open Access Discrete Spherical Harmonic Transforms of Nearly Equidistributed Global Data(Versita, 2011-06) Blais, J. A. RodItem Open Access Discrete Spherical Harmonic Transforms: Numerical Preconditioning and Optimization(2008) Blais, J. A. RodItem Open Access Distributed Geocomputations and Web Collaboration(2009) Blais, J. A. RodItem Open Access Exploring Monte Carlo Simulation Strategies for Geoscience Applications(2008) Blais, J. A. Rod; Grebenitcharsky, R.; Zhang, Z.Item Open Access Exploring Various Monte Carlo Simulations for Geoscience Applications(2010) Blais, J. A. RodItem Open Access Geocomputations and Related Web Services(2008) Blais, J. A. RodItem Open Access Geomatics and the New Cyber-infrastructure(Canadian Institute of Geomatics, 2008) Blais, J. A. Rod; Esche, HaroldItem Open Access Least Squares for Practitioners(2010-09-23) Blais, J. A. RodIn experimental science and engineering, least squares are ubiquitous in analysis and digital data processing applications. Minimizing sums of squares of some quantities can be interpreted in very different ways and confusion can arise in practice, especially concerning the optimality and reliability of the results. Interpretations of least squares in terms of norms and likelihoods need to be considered to provide guidelines for general users. Assuming minimal prerequisites, the following expository discussion is intended to elaborate on some of the mathematical characteristics of the least-squares methodology and some closely related questions in the analysis of the results, model identification, and reliability for practical applications. Examples of simple applications are included to illustrate some of the advantages, disadvantages, and limitations of least squares in practice. Concluding remarks summarize the situation and provide some indications of practical areas of current research and development.Item Open Access Least Squares for Practitioners(Hindawi Publishing Corporation, 2010-08-16) Blais, J. A. RodItem Open Access Lomb-Scargle Spectral Analysis of Nonequispaced Data.(2008) Orlob, M.; Blais, J. A. Rod; Braun, A.Item Open Access Modeling Precipitation Uncertainty Effect on Flood Flows in a Medium Sized Watershed(2010) Mutulu, P.; Blais, J. A. RodItem Open Access Monte Carlo Simulations of Gravimetric Terrain Corrections Using LIDAR Data(2010) Blais, J. A. RodItem Open Access On Monte Carlo Methods and Applications in Geoscience(2009) Zhang, Z.; Blais, J. A. RodItem Open Access Optimal Data Structures for Spherical Multiresolution Analysis and Synthesis(2011) Blais, J. A. RodItem Open Access Optimal Modeling and Filtering of Stochastic Time Series for Geoscience Applications(Hindawi Publishing Corporation, 2013-04-23) Blais, J. A. RodItem Open Access Optimal Modeling and Filtering of Stochastic Time Series for Geoscience Applications(2013-05-16) Blais, J. A. RodSequences of observations or measurements are often modeled as realizations of stochastic processes with some stationary properties in the first and second moments. However in practice, the noise biases and variances are likely to be different for different epochs in time or regions in space, and hence such stationarity assumptions are often questionable. In the case of strict stationarity with equally spaced data, the Wiener-Hopf equations can readily be solved with fast Fourier transforms (FFTs) with optimal computational efficiency. In more general contexts, covariance matrices can also be diagonalized using the Karhunen-Loève transforms (KLTs), or more generally using empirical orthogonal and biorthogonal expansions, which are unfortunately much more demanding in terms of computational efforts. In cases with increment stationarity, the mathematical modeling can be modified and generalized covariances can be used with some computational advantages. The general nonlinear solution methodology is also briefly overviewed with the practical limitations. These different formulations are discussed with special emphasis on the spectral properties of covariance matrices and illustrated with some numerical examples. General recommendations are included for practical geoscience applications.Item Open Access Randomness Characterization in Computing and Stochastic Simulations(2013) Blais, J. A. RodItem Open Access Some Reflections on Advanced Geocomputations and the Data Deluge(2012) Blais, J. A. Rod