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Computer Based Numerical and Statistical Techniques (Hardcover)
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Computer Based Numerical and Statistical Techniques (Hardcover)
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Computer-based numerical and statistical techniques have the
purpose to improve performance and minimize error in
problem-solving application. For example, in signal processing that
considers signals as stochastic processes, using their statistical
properties; in climatology and climate monitoring to attempt for
weather prediction and to reveal alterations in the environment; in
demography where the statistical study of an entire population is
performed, statistical methods can be applied to any kind of
population character that varies over a time or space. For such
reasons, the application of both numerical analysis and statistical
sciences has become a fundamental knowledge of all the modern
engineers and scientists. The contents of this book cover several
advanced applications of numerical and statistical procedures in
many different fields. In particular, numerical stability analysis,
numerical integration methods for differential and integral
equations, numerical differentiation, time-series and images
statistical analysis, and Monte Carlo methods. In the first section
of book, the search of numerical solutions of first-order linear
Fuzzy differential equations, of PDEs in two different problems of
fluid dynamics and heat transfer, of nonlinear Sine-Gordon equation
by modified cubic B-spline collocation method, and of nonlinear
models of electrical transformers is discussed. Moreover, enough
space is given to the analysis of the numerical stability in
weather and climate models, and of the exponential convergence of
particular forms of integral equations. At last, the problems both
of differentiating a noisy and nonsmooth function avoiding the
noise amplification of finite-difference methods, and of the
computational cost of several numerical methods applied for solving
of fractional differential equations are considered.In the second
and last section of the book, different examples of statistical
analysis and of application of Monte Carlo (MC) methods are shown
in several fields. In particular, the statistical study of time
series with scaling indices, and the application of wavelet-based
analysis and a sliding window-based method for extracting
spatiotemporal patterns are discussed. Moreover, the statistical
evaluation both of a fully automated mammographic breast density
algorithm, and of the effect of nano-CMOS spatial variability on
integrated circuits is also studied. Lastly, three different
examples of application of MC are provided: an integrated procedure
for Bayesian inference using Markov chain MC methods; MC numerical
simulations to solve non-stationary random responses of nonlinear
multi-degrees-of-freedom Duffing systems subjected to evolutionary
random excitations; and the comparison of classical MC methods and
deterministic grid-based Boltzmann equation solvers implemented in
a commercial treatment planning system for radiotherapy photon beam
dose calculation.
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