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On the condition number of the . . .

by Marco Donatelli , Martin Hanke - LINEAR ALGEBRA AND ITS APPLICATIONS , 2010
"... ..."
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Condition number of Bott–Duffin inverse and their condition numbers

by Yimin Wei A, Wei Xu B
"... 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 c ..."
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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 fundamental properties of natural numbers

by Grzegorz Bancerek - Journal of Formalized Mathematics , 1989
"... Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1.h ..."
Abstract - Cited by 688 (73 self) - Add to MetaCart
. 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

Tails of condition number distributions

by Alan Edelman, Brian, D. Sutton - SIAM J. Matrix Anal. Appl
"... 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 - Cited by 28 (2 self) - Add to MetaCart
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

Estimating matrix condition numbers

by Dianne Prost O’leary - SIAM J. Sci. Stat. Comput , 1980
"... 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, n ..."
Abstract - Cited by 3 (0 self) - Add to MetaCart
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

LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares

by Christopher C. Paige, Michael A. Saunders - ACM Trans. Math. Software , 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax- b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
Abstract - Cited by 653 (21 self) - Add to MetaCart
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

Smoothed Analysis of Condition Numbers

by Peter Bürgisser
"... 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 and conv ..."
Abstract - Cited by 8 (3 self) - Add to MetaCart
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

Condition numbers of Gaussian random matrices

by Zizhong Chen, Jack, J. Dongarra - SIAM J. Matrix Anal. Appl , 2005
"... 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 ..."
Abstract - Cited by 62 (4 self) - Add to MetaCart
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

Condition number · Search

by Mazen Al, Borno Xiao-wen, Chang Xiaohu Xie, M. Al Borno, X. -w. Chang, X. Xie
"... This paper intends to shed light on the decorrelation or reduction process in solving integer least squares (ILS) problems for ambiguity determination. We show what this process should try to achieve to make the widely used discrete search process fast and explain why neither decreasing correlation ..."
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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

High dimensional graphs and variable selection with the Lasso

by Nicolai Meinshausen, Peter Bühlmann - ANNALS OF STATISTICS , 2006
"... 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 is a ..."
Abstract - Cited by 736 (22 self) - Add to MetaCart
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
Results 1 - 10 of 65,118