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PRECONDITIONS OF FORMATION OF THE COMPETITIVE ENVIRONMENT OF THE REGIONAL REPRODUCTION PROCESS
K. M. Urusova, Irina N. Urusova
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Optimal and Superoptimal Circulant Preconditioners
SIAM Journal on Matrix Analysis and Applications, 1992The author investigates preconditioning methods for linear algebraic systems \(Ax=f\) with a dense positive definite matrix \(A\). He calls a conditioning matrix \(C\) optimal if it minimizes \(\| C-A\|\) and superoptimal if it minimizes \(\| I-C^{-1} A\|\), both in the Frobenius norm.
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Optimal Equivalent Preconditioners
SIAM Journal on Numerical Analysis, 1993Preconditioning strategies for elliptic partial differential operators and their discrete counterparts are compared by a model problem. The technique uses a selfadjoint positive definite operator \(B\) as the preconditioner for the nonselfadjoint convection-diffusion operator \(A\). Preconditioning is done by \(A\)'s leading term plus a positive zeroth
Manteuffel, Thomas, Otto, James
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SIAM Journal on Scientific Computing, 1997
In analogy with the multigrid method, the authors present a solution method for problems based on the \(p\)-version of the finite element method whereby degrees of freedom associated with approximation order \(p\) are visited at once and separately from those of approximation order \(p-1\) and \(p+1\).
Hu, Ning +2 more
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In analogy with the multigrid method, the authors present a solution method for problems based on the \(p\)-version of the finite element method whereby degrees of freedom associated with approximation order \(p\) are visited at once and separately from those of approximation order \(p-1\) and \(p+1\).
Hu, Ning +2 more
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Multiresolution Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing, 2001Summary: We introduce a new preconditioner for elliptic partial differential equations (PDEs) on unstructured meshes. Using a wavelet-inspired basis we compress the inverse of the matrix, allowing an effective sparse approximate inverse by solving the sparsity vs. accuracy conflict. The key issue in this compression is to use second generation wavelets
Bridson, Robert, Tang, Wei-Pai
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Generalized circulant Strang‐type preconditioners
Numerical Linear Algebra with Applications, 2011SUMMARYStrang's proposal to use a circulant preconditioner for linear systems of equations with a Hermitian positive definite Toeplitz matrix has given rise to considerable research on circulant preconditioners. This paper presents an {eiφ}‐circulant Strang‐type preconditioner. Copyright © 2011 John Wiley & Sons, Ltd.
NOSCHESE, Silvia, Lothar Reichel
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An approximate BDDC preconditioner
Numerical Linear Algebra with Applications, 2007AbstractThe balancing domain decomposition by constraints (BDDC) preconditioner requires direct solutions of two linear systems for each substructure and one linear system for a global coarse problem. The computations and memory needed for these solutions can be prohibitive if any one system is too large.
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Circulant Preconditioners Constructed from Kernels
SIAM Journal on Numerical Analysis, 1992The concept of a model operator as a preconditioner is one of the widely used for the solution of large elliptic grid systems. During the last decade it gained a recognition in some ``nonelliptic'' applications like the solution of systems with Toeplitz matrix \(A\) which arise, for example, in signal processing and control theory.
Chan, Raymond H., Yeung, Man-Chung
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