Acta Numerica 2002: Volume 11 (Acta Numerica) by Arieh Iserles

By Arieh Iserles

Acta Numerica anually surveys an important advancements in numerical arithmetic and medical computing. the themes and authors of the great articles are selected via a extraordinary overseas editorial board, on the way to record an important and well timed advancements in a fashion available to the broader neighborhood of execs with an curiosity in clinical computing. Acta Numerica volumes are a beneficial instrument not just for researchers and execs wishing to enhance their realizing of numerical options and algorithms and stick with new advancements. also they are used as complicated instructing aids at schools and universities (many of the unique articles are used because the major source for graduate courses).

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Additional resources for Acta Numerica 2002: Volume 11 (Acta Numerica)

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An}, Let the cardinality £ of the index set C be denoted by |£|. The PEIEP is to determine (complete) values for the n 2 — \C\ positions that do not belong to £ so as to satisfy the spectral constraint. The Jacobi structure can be considered as a special case of PEIEP where, in addition to the desired symmetry of the band, elements outside the tridiagonal band are required to be zero. Another interesting variation of the PEIEP is the completion problem, where only a one-to-one correspondence between the £ positions in C and the £ prescribed values { a i , .

N — 1, if /xi < ••• < \in are eigenvalues of T(0,1,^3,... ,tn). i=\ Mi — 0> it i s necessary that n\ < 0. The range of (p is the simplex The key components in the proof by Landau (1994) are as follows. First, the set T of regular Toeplitz matrices of the form T(0,1, £ 3 , . . , tn) is not empty. STRUCTURED INVERSE EIGENVALUE PROBLEMS 35 Secondly, the map

CHU AND GENE H. GOLUB horizontal displacement of the ith particle at time t. Then it is easy to see that the equation of motion is given by mi + k2(u2 - at - «*)> at at « = 2,... 11). 12). The direct problem calculates the natural frequencies and modes of the mass-sprint system from given values of rrii and kk- The inverse problem requires calculating quantities such as *+ i+1 and , i+1 from the spectral data. Based on this model, we make the following observations. If the last mass mn is fastened to the floor, then the motion of mass m n _i is governed by m n-l i T7 = -kn-l(Un-l ~ Un-2) at instead.

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