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Estimating error norms in CG-like algorithms for least-squares and least-norm problems
In Meurant et al. (Numer. Algorithms 88 (3), 1337–1359,
2021 ), we presented an adaptive estimate for the energy norm of the error in the conjugate...
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Formally-Verified Round-Off Error Analysis of Runge–Kutta Methods
Numerical errors are insidious, difficult to predict and inherent in different levels of critical systems design. Indeed, numerical algorithms...
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Standards and Norms for Measurements
Several standards and norms govern efficient and universally valid principles for measurements. They also form the basis for test metrics.
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Protection of online images against theft using robust multimodal biometric watermarking and T-norms
Online image theft is a severe concern faced by many photographers. It occurs when someone uses the photo they took accidentally or deliberately...
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Error Estimation
Consider first data-based machine learning techniques. They rely on large sets of examples provided during the training stage and do not learn with...
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Triangulations and Error Estimates for Interpolating Lyapunov Functions
The CPA method to compute Lyapunov functions depends on a triangulation of the relevant part of the state space. In more detail, a CPA (Continuous...
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Analysis of Quarantine Norms and Their Healthcare Benefits for Covid-19
The corona virus, which causes COVID-19 disease, is constantly changing its genetic characteristics, and new variants of the virus are expected to...
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A posteriori error bounds for the block-Lanczos method for matrix function approximation
We extend the error bounds from Chen et al. ( SIAM J. Matrix Anal. Appl 43(2):787–811,
2022 ) for the Lanczos method for matrix function approximation...
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A priori error estimates of a discontinuous Galerkin method for the Navier-Stokes equations
This-36pt paper considers a discontinuous Galerkin finite element method for the 2 D transient and incompressible Navier-Stokes model. Following the...
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Differential equation software for the computation of error-controlled continuous approximate solutions
In this paper, we survey selected software packages for the numerical solution of boundary value ODEs (BVODEs), time-dependent PDEs in one spatial...
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Error and optimism bias regularization
In Machine Learning, prediction quality is usually measured using different techniques and evaluation methods. In the regression models, the goal is...
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The effect of intrinsic dimension on the Bayes-error of projected quadratic discriminant classification
High-dimensionality is a common hurdle in machine learning and pattern classification; mitigating its effects has attracted extensive research...
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De-noising boosting methods for variable selection and estimation subject to error-prone variables
Boosting is one of the most powerful statistical learning methods that combines multiple weak learners into a strong learner. The main idea of...
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Residual-based a posteriori error analysis of an ultra-weak discontinuous Galerkin method for nonlinear second-order initial-value problems
In this paper, we propose and analyze implicit residual-based a posteriori error estimates for the ultra-weak discontinuous Galerkin (UWDG) method...
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HS-Based Error Correction Algorithm for Noisy Binary GCD Side-Channel Sequences
The secure implementation of the Greatest Common Divisor (GCD) algorithm is fundamental for many cryptographic schemes. The binary GCD algorithm has...
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Unconditional error estimates of linearized BDF2-Galerkin FEMs for nonlinear coupled Schrödinger-Helmholtz equations
In this paper, we present two linearized BDF2 Galerkin FEMs for the nonlinear and coupled Schrödinger-Helmholtz equations. Different from the...
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Error bounds for septic Hermite interpolation and its implementation to study modified Burgers’ equation
In this paper, the orthogonal collocation technique with septic Hermite splines as basis function is used to find the numerical solution of...
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Global error estimation for explicit second derivative general linear methods
In this paper, we describe an approach to estimate the global error for explicit second derivative general linear methods based on the approach which...
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A priori and a posteriori error analysis for virtual element discretization of elliptic optimal control problem
In this paper, a virtual element method (VEM) discretization of elliptic optimal control problem with pointwise control constraint is investigated....
