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Anwendungsbeispiele Englisch
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- In the case of a system of linear equations, the two main classes of iterative methods are the stationary iterative methods, and the more general Krylov subspace methods.
- His main research interests are Krylov subspace methods, non-normal operators and spectral perturbation theory, Toeplitz matrices, random matrices, and damped wave operators.
- In a large system, we may employ iterative methods such as Krylov subspace methods.
- The method approximates the solution by the vector in a Krylov subspace with minimal residual.
- For more general circuits, the method was considered impractical for all but these very small circuits until the mid-1990s, when Krylov subspace methods were applied to the problem.
- Arnoldi finds an approximation to the eigenvalues and eigenvectors of general (possibly non-Hermitian) matrices by constructing an orthonormal basis of the Krylov subspace, which makes it particularly useful when dealing with large sparse matrices.
- Richard Newton Technical Impact Award in Electronic Design Automation for their paper "Efficient steady-state analysis based on matrix-free Krylov-subspace methods".
- In linear algebra, the order-"r" Krylov subspace generated by an "n"-by-"n" matrix "A" and a vector "b" of dimension "n" is the linear subspace spanned by the images of "b" under the first "r" powers of "A" (starting from [...]), that is, Many linear dynamical system tests in control theory, especially those related to controllability and observability, involve checking the rank of the Krylov subspace.
- First, it was arguably the first RF simulator in that it was the first to be designed for large bipolar and CMOS RF circuits; it used shooting methods as its base algorithm; and it pioneered the use of Krylov subspace methods.
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