Abstract not found

Various normwise relative condition numbers that measure the sensitivity of Bott– Duffin inverse and the solution of constrained linear systems are characterized. The sensitivity of condition number itself is then investigated. Finally, upper bounds are derived for the sensitivity of componentwise

. The scheme Ind concerns a unary predicate P, and states that: For every natural number k holdsP[k] provided the parameters satisfy the following conditions: • P[0], and • For every natural number k such thatP[k] holdsP[k+1]. The scheme Nat Ind concerns a unary predicateP, and states that: For every natural

Abstract. Let κ be the condition number of an m-by-n matrix with independent standard Gaussian entries, either real (β = 1) or complex (β = 2). The major result is the existence of a constant C (depending on m, n, β) such that P [κ> x] < C x −β for all x. As x → ∞, the bound is asymptotically

Abstract. In this note we study certain estimators for the condition number of a matrix which, given an LU factorization of a matrix, are easily calculated. The main observations are that the choice of estimator is very norm-dependent, and that although some simple estimators are consistently bad

numerical properties. Reliable stopping criteria are derived, along with estimates of standard errors for x and the condition number of A. These are used in the FORTRAN implementation of the method, subroutine LSQR. Numerical tests are described comparing I~QR with several other conjugate

The running time of many iterative numerical algorithms is dominated by the condition number of the input, a quantity measuring the sensitivity of the solution with regard to small perturbations of the input. Examples are iterative methods of linear algebra, interior-point methods of linear

Abstract. Let Gm×n be an m × n real random matrix whose elements are independent and identically distributed standard normal random variables, and let κ2(Gm×n) be the 2-norm condition number of Gm×n. We prove that, for any) m ≥ 2, n ≥ 2 and x ≥ |n − m | + 1, κ2(Gm×n) satisfies

coefficients of real least squares (RLS) estimators of the ambiguities nor decreasing the condition number of the covariance matrix of the RLS estimator of the ambiguity vector should be an objective of the reduction process. The new understanding leads to a new reduction algorithm, which avoids some

The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso