scholarly journals Linear convergence in the approximation of rank-one convex envelopes

2004 ◽  
Vol 38 (5) ◽  
pp. 811-820 ◽  
Author(s):  
Sören Bartels
Keyword(s):  
Linear Convergence ◽  
Convex Envelopes ◽  
Rank One

Estimates for numerical approximations of rank one convex envelopes

2000 ◽  
Vol 85 (4) ◽  
pp. 647-663 ◽  
Author(s):  
G. Dolzmann ◽  
N.J. Walkington
Keyword(s):  
Numerical Approximations ◽  
Convex Envelopes ◽  
Rank One

scholarly journals On the continuity of the polyconvex, quasiconvex and rank-oneconvex envelopes with respect to growth condition

1993 ◽  
Vol 123 (4) ◽  
pp. 707-729 ◽  
Author(s):  
Wilfrid Gangbo
Keyword(s):  
Growth Condition ◽  
Convex Envelopes ◽  
Rank One

SynopsisLetCf, Pf, QfandRfbe respectively the convex, polyconvex, quasi-convex and rank-one-convex envelopes of a given functionf. If fp: RNxM→R andfq(ξ) behaves as |ξ|qat infinityq∈ (1, ∞), we show that. This is the case for (Pfp)pprovided thatq≠1,…, min (N, M), otherwise. In the last part of this work, we show thatf(ξ) = g(|ξ|) does not imply in generalPf = Qf.

Derivation of the Wave and Scattering Operators for an Interaction of Rank One

1970 ◽  
Vol 11 (8) ◽  
pp. 2415-2424 ◽  
Author(s):  
M. Anthea Grubb ◽  
D. B. Pearson
Keyword(s):  
Rank One ◽  
Scattering Operators

scholarly journals Ramification Theory for Extensions of Degree p. II

1972 ◽  
Vol 46 ◽  
pp. 97-109
Author(s):  
Susan Williamson
Keyword(s):  
Valuation Ring ◽  
Quotient Field ◽  
Root Of Unity ◽  
Ramification Index ◽  
Ramification Theory ◽  
Rank One ◽  
The Absolute

Let k denote the quotient field of a complete discrete rank one valuation ring R of unequal characteristic and let p denote the characteristic of R̅; assume that R contains a primitive pth root of unity, so that the absolute ramification index e of R is a multiple of p — 1, and each Gallois extension K ⊃ k of degree p may be obtained by the adjunction of a pth root.

scholarly journals Algorithms and Applications to Weighted Rank-one Binary Matrix Factorization

2020 ◽  
Vol 11 (2) ◽  
pp. 1-33
Author(s):  
Haibing Lu ◽  
Xi Chen ◽  
Junmin Shi ◽  
Jaideep Vaidya ◽  
Vijayalakshmi Atluri ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Binary Matrix ◽  
Rank One ◽  
Binary Matrix Factorization ◽  
Weighted Rank

scholarly journals Convergence rate analysis of an iterative algorithm for solving the multiple-sets split equality problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shijie Sun ◽  
Meiling Feng ◽  
Luoyi Shi
Keyword(s):  
Convergence Rate ◽  
Iterative Algorithm ◽  
Sufficient Conditions ◽  
Linear Convergence ◽  
Regularity Property ◽  
Step Size ◽  
Bounded Linear ◽  
Split Equality Problem ◽  
Linear Convergence Rate ◽  
Equality Problem

Abstract This paper considers an iterative algorithm of solving the multiple-sets split equality problem (MSSEP) whose step size is independent of the norm of the related operators, and investigates its sublinear and linear convergence rate. In particular, we present a notion of bounded Hölder regularity property for the MSSEP, which is a generalization of the well-known concept of bounded linear regularity property, and give several sufficient conditions to ensure it. Then we use this property to conclude the sublinear and linear convergence rate of the algorithm. In the end, some numerical experiments are provided to verify the validity of our consequences.

scholarly journals Dimension of the Exceptional Set in the Aronszajn–Donoghue Theorem for Finite Rank Perturbations

2020 ◽  
Author(s):  
Constanze Liaw ◽  
Sergei Treil ◽  
Alexander Volberg
Keyword(s):  
Finite Rank ◽  
Measure Zero ◽  
Adjoint Operator ◽  
Cyclic Vector ◽  
Spectral Measures ◽  
Hermitian Matrices ◽  
Exceptional Set ◽  
Direct Sum ◽  
Rank One Perturbation ◽  
Rank One

Abstract The classical Aronszajn–Donoghue theorem states that for a rank-one perturbation of a self-adjoint operator (by a cyclic vector) the singular parts of the spectral measures of the original and perturbed operators are mutually singular. As simple direct sum type examples show, this result does not hold for finite rank perturbations. However, the set of exceptional perturbations is pretty small. Namely, for a family of rank $d$ perturbations $A_{\boldsymbol{\alpha }}:= A + {\textbf{B}} {\boldsymbol{\alpha }} {\textbf{B}}^*$, ${\textbf{B}}:{\mathbb C}^d\to{{\mathcal{H}}}$, with ${\operatorname{Ran}}{\textbf{B}}$ being cyclic for $A$, parametrized by $d\times d$ Hermitian matrices ${\boldsymbol{\alpha }}$, the singular parts of the spectral measures of $A$ and $A_{\boldsymbol{\alpha }}$ are mutually singular for all ${\boldsymbol{\alpha }}$ except for a small exceptional set $E$. It was shown earlier by the 1st two authors, see [4], that $E$ is a subset of measure zero of the space $\textbf{H}(d)$ of $d\times d$ Hermitian matrices. In this paper, we show that the set $E$ has small Hausdorff dimension, $\dim E \le \dim \textbf{H}(d)-1 = d^2-1$.

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