Convergence Analysis of Gradient Iterations for the Symmetric Eigenvalue Problem
نویسندگان
چکیده
منابع مشابه
Convergence Analysis of Gradient Iterations for the Symmetric Eigenvalue Problem
Gradient iterations for the Rayleigh quotient are simple and robust solvers to determine a few of the smallest eigenvalues together with the associated eigenvectors of (generalized) matrix eigenvalue problems for symmetric matrices. Sharp convergence estimates for the Ritz values and Ritz vectors are derived for various steepest descent/ascent gradient iterations. The analysis shows that poores...
متن کاملSome results on the symmetric doubly stochastic inverse eigenvalue problem
The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$, to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$. If there exists an $ntimes n$ symmetric doubly stochastic ...
متن کاملAsymptotic convergence of spectral inverse iterations for stochastic eigenvalue problems
We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought from a finite dimensional space formed as the tensor product of the approximation space for the underlying stochastic function space, and the approximation spac...
متن کاملThe symmetric eigenvalue complementarity problem
In this paper the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed. It is shown that the symmetric (EiCP) is equivalent to finding an equilibrium solution of a differentiable optimization problem in a compact set. A necessary and sufficient condition for solvability is obtained which, when verified, gives a convenient starting point for any gradient-ascent loc...
متن کاملthe algorithm for solving the inverse numerical range problem
برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.
15 صفحه اولذخیره 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: SIAM Journal on Matrix Analysis and Applications
سال: 2011
ISSN: 0895-4798,1095-7162
DOI: 10.1137/100784928