Factorization of matrix polynomials with multiple roots
نویسندگان
چکیده
منابع مشابه
On Matrix Polynomials with Real Roots
It is proved that the roots of combinations of matrix polynomials with real roots can be recast as eigenvalues of combinations of real symmetric matrices, under certain hypotheses. The proof is based on recent solution of the Lax conjecture. Several applications and corollaries, in particular concerning hyperbolic matrix polynomials, are presented.
متن کاملComputing multiple roots of inexact polynomials
We present a combination of two novel algorithms that accurately calculate multiple roots of general polynomials. For a given multiplicity structure and initial root estimates, Algorithm I transforms the singular root-finding into a regular nonlinear least squares problem on a pejorative manifold, and calculates multiple roots simultaneously. To fulfill the input requirement of Algorithm I, we ...
متن کاملNon-Negative Multiple Matrix Factorization
Non-negative Matrix Factorization (NMF) is a traditional unsupervised machine learning technique for decomposing a matrix into a set of bases and coefficients under the non-negative constraint. NMF with sparse constraints is also known for extracting reasonable components from noisy data. However, NMF tends to give undesired results in the case of highly sparse data, because the information inc...
متن کاملdeterminant of the hankel matrix with binomial entries
abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.
15 صفحه اولTropical Roots as Approximations to Eigenvalues of Matrix Polynomials
The tropical roots of t×p(x) = max0≤j≤` ‖Aj‖x are points at which the maximum is attained at least twice. These roots, which can be computed in only O(`) operations, can be good approximations to the moduli of the eigenvalues of the matrix polynomial P (λ) = ∑` j=0 λ Aj , in particular when the norms of the matrices Aj vary widely. Our aim is to investigate this observation and its applications...
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: Linear Algebra and its Applications
سال: 1985
ISSN: 0024-3795
DOI: 10.1016/0024-3795(85)90067-9