This paper gives perturbation analyses for Q 1 and R in the QR factorization A = Q 1 R, Q T 1 Q 1 = I, for a given real m \Theta n matrix A of rank n. The analyses more accurately reflect the sensitivity of the problem than previous normwise results. The condition numbers here are altered by any

coordinates, such that given sketches C(p) and C(q) one can estimate jp \Gamma qj 1 up to a factor of (1 + ffl) with large probability. This solves the main open problem of [10]. ffl we obtain another sketch function C 0 which maps l n 1 into a normed space l m 1 (as opposed to C), such that m = m

that the majority function does not have a linear-size quantum formula. Keywords. Boolean circuit complexity, communication complexity, quantum communication complexity, quantum computation AMS subject classifications. 68Q05, 68Q15 1 This research was supported in part by the National Science Foundation under

This research examines spatial patterns of manufacturing product innovation and provides a model of factors contributing to geographic concentration of innovation. The model maintains that innovation is related to concentrations of innovative inputs, including: university R&D, industrial R

For given m × n matrix A, with m> n, QR factorization has form A = Q R O where matrix Q is m×m and orthogonal, and R is n × n and upper triangular Can be used to solve linear systems, least squares problems, etc. As with Gaussian elimination, zeros are introduced successively into matrix A

for the MKdV equation leads to a Riemann-Hilbert factorization problem for a 2 × 2 matrix valued function m = m(·; x, t) analytic in C\R, (1) where m+(z) = m−(z)vx,t, z ∈ R, m(z) → I as z → ∞, m±(z) = lim ε↓0 m(z ± iε; x, t), vx,t(z) ≡ e −i(4tz3 +xz)σ3 v(z)e i(4tz 3 +xz)σ3, σ3 =

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

This paper presents a new analysis of the block downdating of a QR or Cholesky factorization in the presence of numerical errors. Let X be a block of rows of the matrix A and let A 1 be the matrix formed from the additional rows of A. Given a matrix R for which A = QR the problem is to find R

QR decomposition is a computationally intensive linear al-gebra operation that factors a matrix A into the product of a unitary matrix Q and upper triangular matrix R. Adap-tive systems commonly employ QR decomposition to solve overdetermined least squares problems. Performance of QR decomposition

Endo-permutation modules as sources of simple modules. (English summary)