Structured condition numbers and backward errors in scalar product spaces
نویسندگان
چکیده
منابع مشابه
Structured Condition Numbers and Backward Errors in Scalar Product Spaces
We investigate the effect of structure-preserving perturbations on the solution to a linear system, matrix inversion, and distance to singularity. Particular attention is paid to linear and nonlinear structures that form Lie algebras, Jordan algebras and automorphism groups of a scalar product. These include complex symmetric, pseudo-symmetric, persymmetric, skewsymmetric, Hamiltonian, unitary,...
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Let A belong to an automorphism group, Lie algebra or Jordan algebra of a scalar product. When A is factored, to what extent do the factors inherit structure from A? We answer this question for the principal matrix square root, the matrix sign decomposition, and the polar decomposition. For general A, we give a simple derivation and characterization of a particular generalized polar decompositi...
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We present a formulation for the structured condition number and for the structured backward error for the linear system A Ax = b, when the rectangular matrix A is subjected to normwise perturbations. Perturbations on the data A and the solution x are measured in the Frobenius norm. Numerical experiments that show the relevance of this condition number in the prediction of the computing error w...
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We characterize the analogues of Householder reflectors in matrix groups associated with scalar products. Examples of such groups include the symplectic and pseudounitary groups. We also precisely delimit the mapping capabilities of these Householder analogues: given a matrix group G and vectors x, y, we give necessary and sufficient conditions for the existence of a Householder-like analogue G...
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2006
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1227