Related papers: End-point corrections for the midpoint rule
The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem approximately, rather than exactly, and in the proof of a…
Researchers often estimate income statistics from summaries that report the number of incomes in bins such as \$0-10,000, \$10,001-20,000,...,\$200,000+. Some analysts assign incomes to bin midpoints, but this treats income as discrete.…
Based on the variable Hilbert scale interpolation inequality bounds for the error of regularisation methods are derived under range inclusions. In this context, new formulae for the modulus of continuity of the inverse of bounded operators…
Based upon the fast computation of the coefficients of the interpolation polynomials at Chebyshev-type points by FFT, DCT and IDST, respectively, together with the efficient evaluation of the modified moments by forwards recursions or by…
Programs with floating-point computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floating-point numbers may differ from the…
A three-point iterative method for solving scalar non-linear equations was selected and then adapted to solve systems of non-linear equations. Subsequently, by applying Taylor's theorem to functions of $\R^{n}$ in $\R^{n}$, it is shown that…
In this paper we present an efficient iterative method of order six for the inclusion of the inverse of a given regular matrix. To provide the upper error bound of the outer matrix for the inverse matrix, we combine point and interval…
Based on a new Taylor-like formula, we derived an improved interpolation error estimate in $W^{1,p}$. We compare it with the classical error estimates based on the standard Taylor formula, and also with the corresponding interpolation error…
The present paper deals with the generalization of Midpoint Ellipse Drawing Algorithm (MPEDA) to minimize the error in the existing MPEDA in cartesian form. In this method, we consider three different values of h, i.e., 1, 0.5 and 0.1. For…
Calibrating a multiclass predictor, that outputs a distribution over labels, is particularly challenging due to the exponential number of possible prediction values. In this work, we propose a new definition of calibration error that…
Large-scale computer experiments are becoming increasingly important in science. A multi-step procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator in multiple steps. In practice, the…
Quasi-Monte Carlo methods are used for numerically integrating multivariate functions. However, the error bounds for these methods typically rely on a priori knowledge of some semi-norm of the integrand, not on the sampled function values.…
Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound algorithms which handle continuous problems. In this paper, we introduce a new strategy to compute very accurate approximations of feasible…
Is perfect error correction always worth the trouble? A framework is presented for the analysis of error detection and correction in multi-level systems of communication that takes into account degrees of freedom attended and ignored by…
Floating-point addition on a finite-precision machine is not associative, so not all mathematically equivalent summations are computationally equivalent. Making this assumption can lead to numerical error in computations. Proper ordering…
This paper discusses the error and cost aspects of ill-posed integral equations when given discrete noisy point evaluations on a fine grid. Standard solution methods usually employ discretization schemes that are directly induced by the…
A new coupling argument is introduced to establish Driver's integration by parts formula and shift Harnack inequality. Unlike known coupling methods where two marginal processes with different starting points are constructed to move…
A new error bound which is better than the current exponential-type error bound is presented in this paper.
In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function $f$ defined on the interval $[a,b]$, this formula is derived by introducing a linear combination of $f'$ computed at $n+1$…
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…