A. Neumaier

Publications334
h-index46
Citations16,627
Highly Influential Citations1,195
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Introduction to Numerical Analysis
1. The numerical evaluation of expressions 2. Linear systems of equations 3. Interpolation and numerical differentiation 4. Numerical integration 5. Univariate nonlinear equations 6. Systems of…
Interval methods for systems of equations
Preface Symbol index 1. Basic properties of interval arithmetic 2. Enclosures for the range of a function 3. Matrices and sublinear mappings 4. The solution of square linear systems of equations 5.…
Restricted maximum likelihood estimation of covariances in sparse linear models
This paper surveys the theoretical and computational development of the restricted maximum likelihood (REML) approach for the estimation of covariance matrices in linear stochastic models. A new…
Global Optimization by Multilevel Coordinate Search
TLDR
A global optimization algorithm based on multilevel coordinate search that is guaranteed to converge if the function is continuous in the neighborhood of a global minimizer is presented.
Distance Regular Graphs
Inequalities are obtained between the various parameters of a distance-regular graph. In particular, if k1 is the valency and k2 is the number of vertices at distance two from a given vertex, then in…
Estimation of parameters and eigenmodes of multivariate autoregressive models
TLDR
Numerical simulations indicate that, with the least squares algorithm, the AR model coefficients and the eigenmodes derived from the coefficients and eigen modes are rough approximations of the confidence intervals inferred from the simulaitons.
Complete search in continuous global optimization and constraint satisfaction
This survey covers the state of the art of techniques for solving general-purpose constrained global optimization problems and continuous constraint satisfaction problems, with emphasis on complete…
RESIDUAL INVERSE ITERATION FOR THE NONLINEAR EIGENVALUE PROBLEM
For the nonlinear eigenvalue problem $A(\hat \lambda )\hat x = 0$, where $A( \cdot )$ is a matrix-valued operator, residual inverse iteration with shift $\sigma $ is defined by \[ a^{(l + 1)} : =…
Solving Ill-Conditioned and Singular Linear Systems: A Tutorial on Regularization
It is shown that the basic regularization procedures for finding meaningful approximate solutions of ill-conditioned or singular linear systems can be phrased and analyzed in terms of classical…
Algorithm 808: ARfit—a matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models
TLDR
The ARfit module that performs the eigendecomposition of a fitted model also constructs approximate confidence intervals for the eigenmodes and their oscillation periods and damping times.
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