Rayleigh Quotient Methods for Estimating Common Roots of Noisy Univariate Polynomials

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Adjusting the Rayleigh Quotient in Semiorthogonal Lanczos Methods Adjusting the Rayleigh Quotient in Semiorthogonal Lanczos Methods

In a semiorthogonal Lanczos algorithm, the orthogonality of the Lanczos vectors is allowed to deteriorate to roughly the square root of the rounding unit, after which the current vectors are reorthogonalized. A theorem of Simon 4] shows that the Rayleigh quotient | i.e., the tridiagonal matrix produced by the Lanczos recursion | contains fully accurate approximations to the Ritz values in spite...

متن کامل

Certified counting of roots of random univariate polynomials

A challenging problem in computational mathematics is to compute roots of a high-degree univariate random polynomial. We combine an efficient multiprecision implementation for solving high-degree random polynomials with two certification methods, namely Smale’s α-theory and one based on Gerschgorin’s theorem, for showing that a given numerical approximation is in the quadratic convergence regio...

متن کامل

Real roots of univariate polynomials and straight line programs

We give a new proof of the NP-hardness of deciding the existence of real roots of an integer univariate polynomial encoded by a straight line program based on certain properties of the Tchebychev polynomials. These techniques allow us to prove some new NP-hardness results related to real root approximation for polynomials given by straight line programs.

متن کامل

Estimating roots of polynomials using perturbation theory

Perturbation theory and the order of magnitude of terms are employed to develop two theorems. The theorems may be useful to estimate the order of magnitude of the roots of a polynomial a priori before solving the equation. The theorems are developed for two special types of polynomials of arbitrary order with their coefficients satisfying certain conditions. Numerical applications of the theore...

متن کامل

Sparse univariate polynomials with many roots over finite fields

Suppose q is a prime power and f ∈ Fq[x] is a univariate polynomial with exactly t nonzero terms and degree <q−1. To establish a finite field analogue of Descartes’ Rule, Bi, Cheng and Rojas (2013) proved an upper bound of 2(q − 1) t−2 t−1 on the number of cosets in F∗ q needed to cover the roots of f in F∗ q . Here, we give explicit f with root structure approaching this bound: For q a t power...

متن کامل

ذخیره 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: Computational Methods in Applied Mathematics

سال: 2018

ISSN: 1609-9389,1609-4840

DOI: 10.1515/cmam-2018-0025