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Condition number of Bott–Duffin inverse and their condition numbers
"... 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
 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 ..."
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Cited by 688 (73 self)
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. 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
 SIAM J. Matrix Anal. Appl
"... Abstract. Let κ be the condition number of an mbyn 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 ..."
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Cited by 28 (2 self)
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Abstract. Let κ be the condition number of an mbyn 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
 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 normdependent, and that although some simple estimators are consistently bad, n ..."
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Cited by 3 (0 self)
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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 normdependent, and that although some simple estimators are consistently bad
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 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 ..."
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Cited by 653 (21 self)
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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
"... 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, interiorpoint methods of linear and conv ..."
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Cited by 8 (3 self)
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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, interiorpoint methods of linear
Condition numbers of Gaussian random matrices
 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 2norm condition number of Gm×n. We prove that, for any) m ≥ 2, n ≥ 2 and x ≥ n − m  + 1, κ2(Gm×n) satisfies ..."
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Cited by 62 (4 self)
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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 2norm 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
"... 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
 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 ..."
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Cited by 736 (22 self)
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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
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