A note on sparse solutions of sparse linear systems
نویسندگان
چکیده
منابع مشابه
On Sparse Solutions of Underdetermined Linear Systems
We first explain the research problem of finding the sparse solution of underdetermined linear systems with some applications. Then we explain three different approaches how to solve the sparse solution: the l1 approach, the orthogonal greedy approach, and the lq approach with 0 < q ≤ 1. We mainly survey recent results and present some new or simplified proofs. In particular, we give a good rea...
متن کاملSparse Solutions of Underdetermined Linear Systems
Ourmain goal here is to discuss perspectives of applications based on solving underdetermined systems of linear equations (SLE). This discussion will include interconnection of underdetermined SLE with global problems of Information Theory and with data measuring and representation. The preference will be given to the description of the hypothetic destination point of the undertaken efforts, th...
متن کاملLinear under-determined systems with sparse solutions: Redirecting a challenge?
Seminal works [8, 14, 15] generated a massive interest in studying linear under-determined systems with sparse solutions. In this paper we give a short mathematical overview of what was accomplished in last 10 years in a particular direction of such a studying. We then discuss what we consider were the main challenges in last 10 years and give our own view as so what are the main challenges tha...
متن کاملEfficient VLSI Implementation of Iterative Solutions to Sparse Linear Systems
We propose a novel way of solving systems of linear equations with sparse coe cient matrices using iterative methods on a VLSI array. The nonzero entries of the coe cient matrix are mapped onto a processor array of size pe pe, where e is the number of nonzero elements, n is the number of equations and e n. The data transport problem that arises because of this mapping is solved using an e cient...
متن کاملFast Verified Solutions of Sparse Linear Systems with H-matrices
This paper is concerned with the problem of verifying the accuracy of an approximate solution of a sparse linear system whose coefficient matrix is an H-matrix. Fast and efficient methods of calculating componentwise error bounds of the computed solution are proposed. The methods are based on the verified criterion for an M-matrix. The main point of this article is that the proposed methods can...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2014
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2014.07.029