A bound for the Moore-Penrose pseudoinverse of a matrix
A combinatorial approach to the conditioning of a single entry in the stationary distribution for a Markov chain.
A Contribution to the Theory of Condition.
A note on estimate of the spectral radius of symmetric matrices
A Symmetric Numerical Range for Matrices.
A theorem on matrices and its applications in functional analysis
A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition
The construction of a well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition is proposed. A suitable parametrix is obtained by using a new unknown and an approximation of the transparency condition. We prove the well-posedness of the equation for any wavenumber. Finally, some numerical comparisons with well-tried method prove the efficiency of the new formulation.
An Algorithm for Scaling Matrices and Computing the Minimum Cycle Mean in a Digraph.
Applications of max algebra to diagonal scaling of matrices.
Characterizations of the distribution of the Demmel condition number of real Wishart matrices
The Demmel condition number is an indicator of the matrix condition, and its properties have recently found applications in many practical problems, such as in MIMO communication systems, in the analytical prediction of level-crossing and fade duration statistics of Rayleigh channels, and in spectrum sensing for cognitive radio systems, among others. As the characterizations of a probability distribution play an important role in probability and statistics, in this paper we study the characterizations...
Condition numbers of Hessenberg companion matrices
The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition number than...
Conditioning properties of the stationary distribution for a Markov chain.
Convergence of -norms of a matrix
a recurrence relation for computing the -norms of an Hermitian matrix is derived and an expression giving approximately the number of eigenvalues which in absolute value are equal to the spectral radius is determined. Using the -norms for the approximation of the spectral radius of an Hermitian matrix an a priori and a posteriori bounds for the error are obtained. Some properties of the a posteriori bound are discussed.
Eigenvalue condition numbers and a formula of Burke, Lewis and Overton.
Estimating the matrix p-norm.
Evaluating the Frechet derivative of the matrix exponential.
High-order finite difference schemes and Toeplitz based preconditioners for elliptic problems.
LDU decompositions with and well conditioned.
Lower Bounds for the Condition Number of Vandermonde Matrices.
Nonsingularity, positive definiteness, and positive invertibility under fixed-point data rounding
For a real square matrix and an integer , let denote the matrix formed from by rounding off all its coefficients to decimal places. The main problem handled in this paper is the following: assuming that has some property, under what additional condition(s) can we be sure that the original matrix possesses the same property? Three properties are investigated: nonsingularity, positive definiteness, and positive invertibility. In all three cases it is shown that there exists a real number...