For B a fixed matrix, we study the problem of using a criterion of Haagerup to find the norm of the map A A·B, where · is the Hadamard or entrywise product of matrices. The techniques developed are applied to triangular truncation, and it is proved that if Kn is the norm of ...
The problem of computing a real matrix perturbation having a minimum norm which causes a general complex matrix to drop rank is examined. Given the state model describing a linear time-invariant system, the norm of this matrix perturbation helps to determine the robustness of several system propert...
The matrix 1-norm estimation algorithm used in LAPACK and various other software libraries and packages has proved to be a valuable tool. However, it has t... A Gerasoulis - 《Mathematics of Computation》 被引量: 108发表: 1988年 Algorithms for constructing (0,1)-matrices with prescribed row...
For a matrix M and vectors x^{(i)}, i\in I, we define \Delta (M;x^{{(i)}}, i\in I) = ||M||_F^2 - ||M - M\sum_{i\in I}x^{(i)}x^{(i)^T}||_F^2 \\ When x^{(i)} are orthonormal vectors, this represents the norm of the projection of M onto the ...
where u is the unit roundoff (throughout we write \(x=o(y)\) to mean \(x\le my\) for a moderate \(m>0\) ), and \(\vert \cdot \vert _l\) is the vector norm of function values at the sample points \(\{\gamma _i\}_{i=1}^l\) , see notation below. classical ...
Low-Rank Representation (LRR) has been a popular tool for identifying data generated from a union of subspaces. It is also known that LRR is computationally challenging. As the size of the nuclear norm regularized matrix of LRR is propor... S Jie,L Ping,H Xu - 《Statistics》 被引量: ...
Here is a not very robust algorithm, but might give you some ideas. Basically it finds where the CDF crosses the 63.2% (mean value for exponential distribution) and outputs the corresponding t. Sometimes it outputs an empty matrix and sometimes more than 1 value, which would have to be adj...
Since for any fixed j, the right-hand side of the equation is hA(p_{j}^{'})– {{t}^{0}}{{h}_{B}}(p_{j}^{'}) = - f(p_{j}^{'}), the norm of the right-hand side in the entire system is not greater than \sqrt {n + 1} M{\kern 1pt} ||{\kern 1pt} p_{...
By default, the estimates are scaled to a unit vector based on the L2-norm. To use a different method, provide an instance of ScalingMethod as a second argument to PowerIteration: <?php use Aboks\PowerIteration\PowerIteration; use Aboks\PowerIteration\ScalingMethod\NormBased; use Aboks\...
WikiMatrix As a result, finding a global optimum of a norm-based objective function is often tractable. Kiel rezulto, trovigo de malloka optimumo de normo-bazita objekta funkcio estas ofte akordiĝema. WikiMatrix 'Well, if that is what you find pleasure in,' said Frodo, 'I pity...