The Ill-conditioning of infinite element stiffness matrices

Deliberate Ill-conditioning of Krylov Matrices Deliberate Ill-conditioning of Krylov Matrices

This paper starts oo with studying simple extrapolation methods for the classical iteration schemes such as Richardson, Jacobi and Gauss-Seidel iteration. The extrapolation procedures can be interpreted as approximate minimal residual methods in a Krylov subspace. It seems therefore logical to consider, conversely, classical methods as pre-processors for Krylov subspace methods, as was done by ...

THE MODEL UPDATING OF MASS, DAMPING AND STIFFNESS MATRICES

Effective Stiffness: Generalizing Effective Resistance Sampling to Finite Element Matrices

We define the notion of effective stiffness and show that it can used to build sparsifiers, algorithms that sparsify linear systems arising from finite-element discretizations of PDEs. In particular, we show that sampling O(n log n) elements according to probabilities derived from effective stiffnesses yields an high quality preconditioner that can be used to solve the linear system in a small ...

Non-additive Lie centralizer of infinite strictly upper triangular matrices

‎Let $mathcal{F}$ be an field of zero characteristic and $N_{infty‎}(‎mathcal{F})$ be the algebra of infinite strictly upper triangular‎ ‎matrices with entries in $mathcal{F}$‎, ‎and $f:N_{infty}(mathcal{F}‎)rightarrow N_{infty}(mathcal{F})$ be a non-additive Lie centralizer of $‎N_{infty }(mathcal{F})$; that is‎, ‎a map satisfying that $f([X,Y])=[f(X),Y]$‎ ‎for all $X,Yin N_{infty}(mathcal{F})...

the model updating of mass, damping and stiffness matrices

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