Question d'inverse - inéquations quotient


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What is a field of quotients of D?

  • Any integral domain Dcan be enlarged to (or embedded in) a ?eld Fsuch that every element of Fcan be expressed as a quotient of two elements of D. (Strictly speaking, every element of F is a quotient of two elements of i[D] where iis as de?ned in Lemma 21.4.) Such a ?eld is a ?eld of quotients of D.
    . Proof.

What is Rayleigh quotient iteration?

  • The idea is to use continually improving eigenvalue estinmLes Lo increa..,€ the rate of convergence of inverse iteration at every step.
    . This algorithm is called Rayleigh quotient iteration.
    . Algorithm 27.3.
    . Rayleigh Quotient Iteration v(O) = some vector with 11,,(0) II = 1 ).(0) = (,,(0) f

What is the initial eigenvector of Rayleigh quotient?

  • RAYLEIGH QUOTIENT, INVERSE ITERATION 209 and let v(O) = (1, 1, l)T / V3 be the initial eigenvector estimate.
    . When Rayleigh quotient iteration is applied to A, the following values A(k) arc computed by t.he first three it.erations:

What is inverse iteration?

  • Inverse iteration is one of the most valuable tools of numerical linear al- gebra, for it is the standard rnethod of ealculating one or IIlOr€eigenvectors of a mat.rix if t.he eigenvalues arc already known.
    . In t.his case Algorit.hm 27.2 is applied as written, exeept.










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