Masterproef T898 : Orthogonale veeltermen en lineaire algebra
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Begeleiding:
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Onderzoeksgroep:
Numerieke Approximatie en Lineaire Algebra Groep
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Herkomst:
Joint proposal (NALAG-Carlos III) made up for a student on Erasmus.
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Context:
Orthogonal polynomials on the unit circle with respect to a positive measure can be transformed into Orthogonal polynomials orthogonal with respect to
a modified measure.
Three classical spectral transformations can be considered:
Christoffel (multiply with |z-α|^2); Geronimus (divide by |z-α|^2 and add a weight at two points) and Uvarov (add a weight at two points).
For the transformation it suffices to compute the Verblunsky coefficients
for the modified measure (that are the recurrence coefficients of the
orthogonal polynomials). These modified coefficients can be computed
by QR or RQ factorizations of a quasi-unitary GGT matrix (that is the matrix
capturing the recursion). In view of the special structure of this matrix
these operations can be performed in O(n) elementary orthogonal Givens transforms.
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Doel:
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Uitwerking:
For the theoretical background, the know-how of the Spanish promotor
can be applied, while on Erasmus during the first semester.
For the aspect of structured matrices and the numerical analysis,
the knowledge of the NALAG research team is available.
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Relevante Literatuur:
Will be made available.
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Profiel:
De student moet redelijk onafhankelijk kunnen werken. Deze masterproef is voor 1 student. Deze masterproef kan gekozen worden door
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Clusters waarin dit onderwerp voorkomt:
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