In many applications of genetic algorithms, there is a tradeoff between speed and accuracy in fitness evaluations when evaluations use numerical methods with varying discretization. In these types of applications, the cost and accuracy vary from discretization errors when implicit or explicit quadrature is used to estimate the function evaluations. This paper examines discretization scheduling,...

We propose a new genetic fuzzy discretization method with feature selection for the pattern classification problems. Traditional discretization methods categorize a continuous attribute into a number of bins. Because they are made on crisp discretization, there exists considerable information loss. Fuzzy discretization allows overlapping intervals and reflects linguistic classification. However...

The area of knowledge discovery and data mining is growing rapidly. A large number of methods are employed to mine knowledge. Many of the methods rely of discrete data. However, most of the datasets used in real application have attributes with continuous values. To make the data mining techniques useful for such datasets, discretization is performed as a preprocessing step of the data mining. ...

We prove the convergence of a hybrid discretization to the viscosity solution of the elliptic Monge-Ampère equation. The hybrid discretization uses a standard finite difference discretization in parts of the computational domain where the solution is expected to be smooth and a monotone scheme elsewhere. A motivation for the hybrid discretization is the lack of an appropriate Newton solver for ...

There is a tradeoff between speed and accuracy in fitness evaluations when various discretization sizes are used to estimate the fitness. This paper introduces discretization scheduling, which varies the size of the discretization within the GA, and compares this method to using a constant discretization. It will be shown that when scheduling the discretization, less computation time is used wi...

We investigate why discretization is effective in naive-Bayes learning. We prove a theorem that identifies particular conditions under which discretization will result in naiveBayes classifiers delivering the same probability estimates as would be obtained if the correct probability density functions were employed. We discuss the factors that might affect naive-Bayes classification error under ...

In chemical engineering, several processes are represented by singular boundary value problems. In general, classical numerical methods fail to produce good approximations for the singular boundary value problems. In this paper, Chebyshev finite difference (ChFD) method and DTM-Pad´e method, which is a combination of differential transform method (DTM) and Pad´e approximant, are applied for sol...

Despite advancements in specifying 3D internal microstructure of reservoir rocks, identifying some sensitive phenomenons are still problematic particularly due to image resolution limitation. Discretization study on such CT-scan data always has encountered with such conflicts that the original data do not fully describe the real porous media. As an alternative attractive approach, one can recon...

In this paper, we explore the Lax-Wendroff (LW) type time discretization as an alternative procedure to the high order Runge-Kutta time discretization adopted for the high order essentially non-oscillatory (ENO) Lagrangian schemes developed in [2, 4]. The LW time discretization is based on a Taylor expansion in time, coupled with a local CauchyKowalewski procedure to utilize the partial differe...

Abstract We develop a new method of discretization and anti-discretization of weighted inequalities which we apply to norms in classical Lorentz spaces and to spaces endowed with the so-called Hilbert norm. Main applications of our results include new integral conditions characterizing embeddings Γp(v) ↪→ Γq(w) and Γp(v) ↪→ Λq(w) and an integral characterization of the associate space to Γp(v),...