Numerical Linear Algebra: An Introduction

@inproceedings{Wendland2017NumericalLA,
  title={Numerical Linear Algebra: An Introduction},
  author={Holger Wendland},
  year={2017}
}
The Sassenfeld criterion revisited
TLDR
The purpose of the present paper is to shed new light on Sassenfeld's criterion and to demonstrate that the original work can be perceived as a special case of a far more extensive concept in the context of preconditioners and iterative linear solvers.
University of Birmingham On the transient planar contact problem in the presence of dry friction and slip
. This article models a plane strain dynamic contact problem for an infinite elastic body. Contact is established for x > 0 under the action of a time-dependent remote compressive load, and the system
Optimization Basics: A Machine Learning View
TLDR
This chapter will make a special effort to show how least-squares regression is so foundational to machine learning.
On the transient planar contact problem in the presence of dry friction and slip
Singular Value Decomposition
  • C. Aggarwal
  • Mathematics
    Linear Algebra and Optimization for Machine Learning
  • 2020
In Chapter 3, we learned that certain types of matrices, which are referred to as positive semidefinite matrices, can be expressed in the following form: $$\displaystyle A= V \varDelta V^T $$
Efficient spherical near‐field antenna measurement using CS method with sparsity estimation
TLDR
The sparsity estimation method is used to estimate the sparsity level of an arbitrary antenna's near field with a few numbers of measurements, which makes the CS method efficient and affordable in the near-field measurement technique.
Random burst sensing of neurotransmitters
TLDR
A random sensing approach to neurotransmitter detection that provides concurrent, co-localized detection of dopamine, serotonin, norepinephrine and pH and works using electrophysiological probes in routine use in clinical preparations thus transforming these and similar electrodes into ultra-fast sources of multi-transmitter information.
Metrics for next-generation gravitational-wave detectors
Gravitational-wave astrophysics has the potential to be transformed by a global network of longer, colder, and thus more sensitive detectors. This network must be constructed to address a wide range
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References

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Hierarchical Matrices: Algorithms and Analysis
This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g.,
Multi-grid methods and applications
  • W. Hackbusch
  • Mathematics
    Springer series in computational mathematics
  • 1985
TLDR
This paper presents the Multi-Grid Method of the Second Kind, a method for solving Singular Perturbation Problems and Eigenvalue Problems and Singular Equations of the Two-Grid Iteration.
Iterative Solution of Large Sparse Systems of Equations
In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods
Singular value decomposition and least squares solutions
TLDR
The decomposition of A is called the singular value decomposition (SVD) and the diagonal elements of ∑ are the non-negative square roots of the eigenvalues of A T A; they are called singular values.
On the rate of convergence of the preconditioned conjugate gradient method
SummaryWe derive new estimates for the rate of convergence of the conjugate gradient method by utilizing isolated eigenvalues of parts of the spectrum. We present a new generalized version of an
Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method
We characterize the class $CG(s)$ of matrices A for which the linear system $A{\bf x} = {\bf b}$ can be solved by an s-term conjugate gradient method. We show that, except for a few anomalies, the
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