Condition numbers of random matrices
نویسنده
چکیده
منابع مشابه
Condition Numbers of Random Toeplitz and Circulant Matrices
Estimating the condition numbers of random structured matrices is a well known challenge (cf. [SST06]), linked to the design of efficient randomized matrix algorithms in [PGMQ], [PIMR10], [PQ10], [PQ12], [PQZa], [PQa], [PQZb], [PQZC], [PY09]. We deduce such estimates for Gaussian random Toeplitz and circulant matrices. The former estimates can be surprising because the condition numbers grow ex...
متن کاملTR-2012013: Condition Numbers of Random Toeplitz and Circulant Matrices
Estimating the condition numbers of random structured matrices is a well known challenge (cf. [SST06]), linked to the design of efficient randomized matrix algorithms in [PGMQ], [PIMR10], [PQ10], [PQ12], [PQZa], [PQa], [PQZb], [PQZC], [PY09]. We deduce such estimates for Gaussian random Toeplitz and circulant matrices. The former estimates can be surprising because the condition numbers grow ex...
متن کاملCondition Numbers of Random Triangular Matrices
Let L n be a lower triangular matrix of dimension n each of whose nonzero entries is an independent N(0; 1) variable, i.e., a random normal variable of mean 0 and variance 1. It is shown that n , the 2-norm condition number of L n , satisses n p n ! 2 almost surely as n ! 1. This exponential growth of n with n is in striking contrast to the linear growth of the condition numbers of random dense...
متن کاملTR-2014009: Estimating the Norms of Random Circulant and Toeplitz Matrices and Their Inverses II
We combine some basic techniques of linear algebra with some expressions for Toeplitz and circulant matrices and the properties of Gaussian random matrices to estimate the norms of Gaussian Toeplitz and circulant random matrices and their inverses. In the case of circulant matrices we obtain sharp probabilistic estimates, which show that the matrices are expected to be very well conditioned. Ou...
متن کاملCompressive Sensing and Structured Random Matrices
These notes give a mathematical introduction to compressive sensing focusing on recovery using `1-minimization and structured random matrices. An emphasis is put on techniques for proving probabilistic estimates for condition numbers of structured random matrices. Estimates of this type are key to providing conditions that ensure exact or approximate recovery of sparse vectors using `1-minimiza...
متن کاملTR-2013015: Estimating the Norms of Random Circulant and Toeplitz Matrices and Their Inverses
We estimate the norms of standard Gaussian random Toeplitz and circulant matrices and their inverses, mostly by means of combining some basic techniques of linear algebra. In the case of circulant matrices we obtain sharp probabilistic estimates, which show that these matrices are expected to be very well conditioned. Our probabilistic estimates for the norms of standard Gaussian random Toeplit...
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ورودعنوان ژورنال:
- J. Complexity
دوره 7 شماره
صفحات -
تاریخ انتشار 1991