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

By Arieh Iserles

Acta Numerica anually surveys an important advancements in numerical arithmetic and medical computing. the themes and authors of the sizeable articles are selected via a distinct overseas editorial board, as a way to document crucial and well timed advancements in a way obtainable to the broader neighborhood of pros with an curiosity in medical computing. Acta Numerica volumes are a invaluable software not just for researchers and execs wishing to improve their figuring out of numerical recommendations and algorithms and stick with new advancements. also they are used as complex instructing aids at faculties and universities (many of the unique articles are used because the major source for graduate courses).

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

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1996). Friedland and Melkman (1979) limited the consideration of NIEPs to symmetric tridiagonal structure. A simple result can be established. 3. (Friedland and Melkman 1979) A set of real numbers Ai > A2 > • • • > An is the spectrum of an n x n nonnegative tridiagonal matrix if and only if Aj + A n _j + i = 0 for all i. In this case, the matrix is given by J = diag(4i, • • • , A^n+1y2]), where 1 f A- + A _• A- - A _• 1 I I Ai — An _j-|-l Ai -f- /\n _j-f-l and Ai = [Aj], if i = (n + l)/2 and n is odd.

Such a formulation offers a handle for numerical computation by optimization techniques. In Chu and Driessel (1991), the dynamical system [^ =[X,[X,Y)}, resulting from projected gradient flow, was studied as a possible numerical means for solving the SNIEP. It is interesting to note that, even if the SNIEP is not solvable, the limit point of the gradient flow gives rise to a least squares solution. 2. 7. Stochastic inverse eigenvalue problems An nxn nonnegative matrix is a (row) stochastic matrix if all its row sums are 1.

On the other hand, we could formulate the SNIEP as a constrained optimization problem of minimizing the objective function F(Q,R):=±\\QTAQ-RoR\\2, subject to the constraint (Q,R) € O{n) x S(n), where o stands for the STRUCTURED INVERSE EIGENVALUE PROBLEMS 41 Hadamard product and S(n) stands for the subspace of n x n symmetric matrices. The idea is to parametrize any symmetric matrix X = QTAQ that is isospectral to A by the orthogonal matrix Q and to parametrize any symmetric nonnegative matrix Y = R o R by the symmetric matrix R via entry-wise squares.

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