Results 1  10
of
50
Mathematik Componentwise perturbation analyses
, 1999
"... Summary. This paper gives componentwise perturbation analyses for Q and R in the QR factorization A = QR, QTQ = I, R upper triangular, for a given real m × n matrix A of rank n. Suchspecific analyses are important for example when the columns of A are badly scaled. First order perturbation bounds ar ..."
Abstract
 Add to MetaCart
Summary. This paper gives componentwise perturbation analyses for Q and R in the QR factorization A = QR, QTQ = I, R upper triangular, for a given real m × n matrix A of rank n. Suchspecific analyses are important for example when the columns of A are badly scaled. First order perturbation bounds
Componentwise Perturbation Analyses for the QR Factorization
"... This paper gives componentwise perturbation analyses for Q and R in the QR factorization A = QR, Q T Q = I, R upper triangular, for a given real m n matrix A of rank n. Such specic analyses are important for example when the columns of A are badly scaled. First order perturbation bounds are given ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
This paper gives componentwise perturbation analyses for Q and R in the QR factorization A = QR, Q T Q = I, R upper triangular, for a given real m n matrix A of rank n. Such specic analyses are important for example when the columns of A are badly scaled. First order perturbation bounds
A Survey of Componentwise Perturbation Theory in Numerical Linear Algebra
 in Mathematics of Computation 19431993: A Half Century of Computational Mathematics
, 1994
"... . Perturbation bounds in numerical linear algebra are traditionally derived and expressed using norms. Norm bounds cannot reflect the scaling or sparsity of a problem and its perturbation, and so can be unduly weak. If the problem data and its perturbation are measured componentwise, much smaller an ..."
Abstract

Cited by 26 (0 self)
 Add to MetaCart
. Perturbation bounds in numerical linear algebra are traditionally derived and expressed using norms. Norm bounds cannot reflect the scaling or sparsity of a problem and its perturbation, and so can be unduly weak. If the problem data and its perturbation are measured componentwise, much smaller
Componentwise Perturbation Theory for Linear Systems with Multiple RightHand Sides
, 1992
"... Existing definitions of componentwise backward error and componentwise condition number for linear systems are extended to systems with multiple righthand sides and to a general class of componentwise measures of perturbations involving Hölder pnorms. It is shown that for a system of order n with ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
Existing definitions of componentwise backward error and componentwise condition number for linear systems are extended to systems with multiple righthand sides and to a general class of componentwise measures of perturbations involving Hölder pnorms. It is shown that for a system of order n
Structured perturbations part II: Componentwise distances
 SIAM J. Matrix Anal. Appl
, 2003
"... Abstract. In the second part of this paper we study condition numbers with respect to componentwise perturbations in the input data for linear systems and for matrix inversion, and the distance to the nearest singular matrix. The structures under investigation are linear structures, namely symmetri ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
Abstract. In the second part of this paper we study condition numbers with respect to componentwise perturbations in the input data for linear systems and for matrix inversion, and the distance to the nearest singular matrix. The structures under investigation are linear structures, namely
Componentwise Distance to Singularity
"... Abstract: A perturbation matrix A = A is considered, where A 2 IR n;n and 0 2 IR n;n. The matrix A is singular i A contains a real singular matrix. A problem is to decide if A is singular or nonsingular, a NPhard problem. The decision can be made by the computation of the componentwise distance to ..."
Abstract
 Add to MetaCart
Abstract: A perturbation matrix A = A is considered, where A 2 IR n;n and 0 2 IR n;n. The matrix A is singular i A contains a real singular matrix. A problem is to decide if A is singular or nonsingular, a NPhard problem. The decision can be made by the computation of the componentwise distance
Componentwise energy amplification in channel flows
, 2004
"... We study the linearized Navier–Stokes (LNS) equations in channel flows from an input–output point of view by analysing their spatiotemporal frequency responses. Spatially distributed and temporally varying body force fields are considered as inputs, and components of the resulting velocity fields a ..."
Abstract
 Add to MetaCart
the effectiveness of input field components, and on the other, the energy content of velocity perturbation components. We establish that wallnormal and spanwise forces have much stronger influence on the velocity field than streamwise force, and that the impact of these forces is most powerful on the streamwise
Rigorous perturbation bounds for some matrix factorizations
 SIAM J. Matrix Anal. Appl
"... Abstract. This article presents rigorous normwise perturbation bounds for the Cholesky, LU and QR factorizations with normwise or componentwise perturbations in the given matrix. The considered componentwise perturbations have the form of backward rounding errors for the standard factorization algor ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
Abstract. This article presents rigorous normwise perturbation bounds for the Cholesky, LU and QR factorizations with normwise or componentwise perturbations in the given matrix. The considered componentwise perturbations have the form of backward rounding errors for the standard factorization
Componentwise Fast Convergence in the Solution of FullRank Systems of Nonlinear Equations
, 2000
"... The asymptotic convergence of parameterized variants of Newton's method for the solution of nonlinear systems of equations is considered. The original system is perturbed by a term involving the variables and a scalar parameter which is driven to zero as the iteration proceeds. The exact local ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
The asymptotic convergence of parameterized variants of Newton's method for the solution of nonlinear systems of equations is considered. The original system is perturbed by a term involving the variables and a scalar parameter which is driven to zero as the iteration proceeds. The exact local
BIT 39(1), pp. 143–151, 1999 ILLCONDITIONEDNESS NEEDS NOT BE COMPONENTWISE NEAR TO ILLPOSEDNESS FOR LEAST SQUARES PROBLEMS
"... Abstract. The condition number of a problem measures the sensitivity of the answer to small changes in the input, where “small ” refers to some distance measure. A problem is called illconditioned if the condition number is large, and it is called illposed if the condition number is infinity. It i ..."
Abstract
 Add to MetaCart
that this is no longer true for least squares problems and other problems involving rectangular matrices. Problems are identified which are arbitrarily illconditioned (in a componentwise sense) whereas any componentwise relative perturbation less than 1 cannot produce an illposed problem. Bounds are given using
Results 1  10
of
50