We analyze the Lanczos method for matrix function approximation (Lanczos-FA), an iterative algorithm computing $f(\mathbf{A}) \mathbf{b}$ when $\mathbf{A}$ is a Hermitian and $\mathbf{b}$ given vector. Assuming that $f : \mathbb{C} \rightarrow \mathbb{C}$ piecewise analytic, we give framework, based on Cauchy integral formula, which can be used to derive priori posteriori error bounds Lanczos-F...

In this paper a spline based integral approximation is utilized to propose sequence of approximations the error function that converge at significantly faster manner than default Taylor series. The can be improved by utilizing erf(x) approximately equal one for x>>1. Two generalizations are possible, first on demarcating integration interval into m equally spaced sub-intervals. second, it large...

This article studies the convolutional kernel function of fractal operators in bone fibers. On basis micro-nano composite structure compact bone, we abstracted physical space fibers and derived operators. The aims to construct analytical expression proves that error is core component convolution In other words, mechanics fractional controlled by function.

In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. Suppose that the lifetimes have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ISE). In this paper, we derive a central limit theorem for t...

let be a random sample from a normal distribution with unknown mean and known variance the usual estimator of the mean, i.e., sample mean is the maximum likelihood estimator which under squared error loss function is minimax and admissible estimator. in many practical situations, is known in advance to lie in an interval, say for some in this case, the maximum likelihood estimator changes and d...