Source: Dissertation Abstracts International, Volume: 37-07, Section: B, page: 3462. / Thesis (Ph.D.)--The Florida State University, 1976.

Source: Dissertation Abstracts International, Volume: 37-08, Section: B, page: 3992. / Thesis (Ph.D.)--The Florida State University, 1976.

Source: Dissertation Abstracts International, Volume: 39-11, Section: B, page: 5410. / Thesis (Ph.D.)--The Florida State University, 1978.

Source: Dissertation Abstracts International, Volume: 35-08, Section: B, page: 4030. / Thesis (Ph.D.)--The Florida State University, 1974.

Source: Dissertation Abstracts International, Volume: 39-06, Section: B, page: 2834. / Thesis (Ph.D.)--The Florida State University, 1978.

Source: Dissertation Abstracts International, Volume: 35-02, Section: B, page: 0933. / Thesis (Ph.D.)--The Florida State University, 1974.

Source: Dissertation Abstracts International, Volume: 35-02, Section: B, page: 0936. / Thesis (Ph.D.)--The Florida State University, 1974.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007. / Includes bibliographical references (p. 51-52). / Can one compute a low-dimensional representation of any given data by looking only at its small sample, chosen cleverly on the fly? Motivated by the above question, we consider the problem of low-rank matrix approximation: given a matrix A..., one wants to compute a rank-k matrix (where k << min{m, n}) nearest to A in the Frobenius norm (also known as the Hilbert-Schmidt norm). We prove that using a sample of roughly O(k/[epsilon]) rows of A one can compute, with high probability, a (1 + [epsilon])-approximation to the nearest rank-k matrix. This gives an algorithm for low-rank approximation with an improved error guarantee (compared to the additive [epsilon]... guarantee known earlier from the work of Frieze, Kannan, and Vempala) and running time O(Mk/[epsilon]), where M is the number of non-zero entries of A. The proof is based on two sampling techniques called adaptive sampling and volume sampling, and some linear algebraic tools. Low-rank matrix approximation under the Frobenius norm is equivalent to the problem of finding a low-dimensional subspace that minimizes the sum of squared distances to given points. The general subspace approximation problem asks one to find a low-dimensional subspace that minimizes the sum of p-th powers of distances (for p > 1) to given points. We generalize our sampling techniques and prove similar sampling-based dimension reduction results for subspace approximation. However, the proof is geometric. / by Amit Jayant Deshpande. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007. / Includes bibliographical references (p. 77-78). / The main result of this thesis is the computation of ... for ... These RO(S¹)-graded TR-groups are the equivariant homotopy groups naturally associated to the S¹-spectrum THH(Fp), the topological Hochschild S¹-spectrum. This computation, which extends a partial result of Hesselholt and Madsen, provides the first example of the RO(S¹)-graded TR-groups of a ring. In particular, we compute the groups ... for all even dimensional representations a, and the order of these groups for odd dimensional [alpha]. These groups arise in algebraic K-theory computations, and are particularly important to the understanding of the algebraic K-theory of non-regular schemes. We also study RO(S¹)-graded TR-theory as an RO(S¹)-graded Mackey functor. Using Lewis and Mandell's homological algebra tools for graded Mackey functors, we provide examples of how Kunneth spectral sequences can be used to understand RO(S¹)-graded TR. / by Teena Meredith Gerhardt. / Ph.D.

University of Macau / Faculty of Science and Technology. / Department of Computer and Information Science