11 [1] In this study, we investigate the significance of using an 12 improved error modeling strategy to characterize the spatio13 temporal characteristics of uncertainty in simulation of soil 14 moisture fields from an off-line land surface model forced 15 with satellite rainfall data. We coupled a Two-Dimensional 16 Satellite Rainfall Error Model (SREM2D) with the Common 17 Land Model to prop...

Abstract. The main theme of this paper is error analysis for approximations derived from two variants of dimensional decomposition of a multivariate function: the referential dimensional decomposition (RDD) and analysisof-variance dimensional decomposition (ADD). New formulae are presented for the lower and upper bounds of the expected errors committed by bivariately and arbitrarily truncated R...

We develop a new theoretical framework to analyze the generalization error of deep learning, and derive a new fast learning rate for two representative algorithms: empirical risk minimization and Bayesian deep learning. The series of theoretical analyses of deep learning has revealed its high expressive power and universal approximation capability. Although these analyses are highly nonparametr...

This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...

A new two-step implicit linear Obrechkoff twelfth algebraic order method with vanished phase-lag and its first, second, third and fourth derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial Schrodinger equation and related problems. This algorithm belongs in the category of the multist...

The display of three dimensional geological body can visually describe the complex subsurface geological structure, effectively improve the engineer's space imagination and intuitively understand the geological spatial relationship. Through analysis of commonly used three dimensional geological data model and considered the impact of faults. The paper establishes a generalized triangular prism ...