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Mar 25, 2018 · Understanding the Generalized Conjugate Residual (GCR) method. I'm given the following description of the GCR algorithm: I think I understand all the steps until: β = (vi,ri−1) ui:= ui−1 + βsi β = (v i, r i − 1) u i:= u i − 1 + β s i. Question: What does βsi β s i look like? Should I compute βsi = visi1 +ri−1si2 β s i = v i s 1 i + r i − 1 s 2 i?

In this paper we analyze the numerical behavior of several minimum residual meth-ods, which are mathematically equivalent to the GMRES method.

Mar 7, 2021 · The difference comes from the fact that GMRES uses an orthonormal basis to build the approximations and GCR uses a $A^TA$ orthogonal basis. My question is why does it matter so much which basis we use and for which examples one method may be better than the other?

A GCR algebra is a C*-algebra $A$ such that $\mathrm{CCR}(A/J)\neq 0$ for all ideals $J\neq A$. Basically this means that the irreducible representations of C*-algebras contain all compact operators. In particular, finite dimensional C*-algebras …

A new method named FT-GCR is proposed here that supplies the preconditioned Generalized Conjugate Residual Krylov solver with detection of, and recovery from, soft faults.

Mar 12, 2021 · A new method named FT-GCR is proposed here that supplies the preconditioned Generalized Conjugate Residual Krylov solver with detection of, and recovery from, soft faults. The algorithm tests on the monotonic decrease of the residual norm and, upon failure, restarts the iteration within the local Krylov space.

arXiv:1901.06056v2 [math.OA] 10 Aug 2019 GCR AND CCR STEINBERG ALGEBRAS LISA ORLOFF CLARK, BENJAMIN STEINBERG, AND DANIEL W VAN WYK Abstract. Kaplansky introduced the notions of CCR and GCR C∗-algebras because they have a tractable representation theory. Many years later, he introduced the notions of CCR and GCR rings. In this

In this paper we characterize when the algebra of an ample groupoid over a field is CCR and GCR. The results turn out to be exact analogues of the corresponding characterization of locally compact groupoids with CCR and GCR $C^{\ast }$ -algebras.

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