Numerical Computation of Rank-One Convex Envelopes
نویسندگان
چکیده
منابع مشابه
Numerical Computation of Rank - One Convex
We describe an algorithm for the numerical computation of the rank-one convex envelope of a function f : Mm×n → R. We prove its convergence and an error estimate in L∞.
متن کاملLinear Convergence in the Approximation of Rank-one Convex Envelopes
A linearly convergent iterative algorithm that approximates the rank-1 convex envelope f of a given function f : Rn×m → R, i.e. the largest function below f which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington. Mathematics Subject Classification. 65K10, 74G15, 74G65, 74N99. Received: May 27...
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Abstract. It is known that the i-th order laminated microstructures can be resolved by the k-th order rank-one convex envelopes with k ≥ i. So the requirement of establishing an efficient numerical scheme for the computation of the finite order rank-one convex envelopes arises. In this paper, we develop an iterative scheme for such a purpose. The 1-st order rank-one convex envelope R1f is appro...
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In this paper we consider the classical problem of finding a low rank approximation of a given matrix. In a least squares sense a closed form solution is available via factorization. However, with additional constraints, or in the presence of missing data, the problem becomes much more difficult. In this paper we show how to efficiently compute the convex envelopes of a class of rank minimizati...
متن کاملOn the Local Structure of Rank-one Convex Hulls
In this note we prove that if K is a compact set of m×n matrices containing an isolated point X with no rank-one connection into the convex hull of K \ {X}, then the rank-one convex hull separates as K = ( K \ {X} )rc ∪ {X}. This is an extension of a result of P. Pedregal, which holds for 2× 2 matrices.
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 1999
ISSN: 0036-1429,1095-7170
DOI: 10.1137/s0036142997325581