Knowledge can be modeled and computed using computational mathematical
methods, then lead to real world conclusions. The strongly related to
that Computational Analysis is a very large area with lots of
applications. This monograph includes a great variety of topics of
Computational Analysis. We present: probabilistic wavelet
approximations, constrained abstract approximation theory, shape
preserving weighted approximation, non positive approximations to
definite integrals, discrete best approximation, approximation theory of
general Picard singular operators including global smoothness
preservation property, fractional singular operators. We also deal with
non-isotropic general Picard singular multivariate operators and
q-Gauss-Weierstrass singular q-integral operators. We talk about
quantitative approximations by shift-invariant univariate and
multivariate integral operators, nonlinear neural networks
approximation, convergence with rates of positive linear operators,
quantitative approximation by bounded linear operators, univariate and
multivariate quantitative approximation by stochastic positive linear
operators on univariate and multivariate stochastic processes. We
further present right fractional calculus and give quantitative
fractional Korovkin theory of positive linear operators. We also give
analytical inequalities, fractional Opial inequalities, fractional
identities and inequalities regarding fractional integrals. We further
deal with semi group operator approximation, simultaneous Feller
probabilistic approximation. We also present Fuzzy singular operator
approximations. We give transfers from real to fuzzy approximation and
talk about fuzzy wavelet and fuzzy neural networks approximations, fuzzy
fractional calculus and fuzzy Ostrowski inequality. We talk about
discrete fractional calculus, nabla discrete fractional calculus and
inequalities. We study the q-inequalities, and q-fractional
inequalities. We further study time scales: delta and nabla approaches,
duality principle and inequalities. We introduce delta and nabla time
scales fractional calculus and inequalities. We finally study
convergence with rates of approximate solutions to exact solution of
multivariate Dirichlet problem and multivariate heat equation, and
discuss the uniqueness of solution of general evolution partial
differential equation \ in multivariate time. The exposed results are
expected to find applications to: applied and computational mathematics,
stochastics, engineering, artificial intelligence, vision, complexity
and machine learning. This monograph is suitable for graduate students
and researchers.
