Computation of Bounds for the Positive Eigenvector of a Nonnegative Irreducible Matrix by Monotone Iteration

نویسنده

  • By W. Bunse
چکیده

A method for the computation of iterative bounds for the positive eigenvector of a nonnegative irreducible matrix is presented. It is based on the P-boundedness of the corresponding fixed point operator. Admissible initial bounds can be obtained by conditional preiteration.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Necessary and Sufficient Condition for Existence of a Positive Perron Vector

In 1907, Oskar Perron showed that a positive square matrix has a unique largest positive eigenvalue with a positive eigenvector. This result was extended to irreducible nonnegative matrices by Geog Frobenius in 1912, and to irreducible nonnegative tensors and weakly irreducible nonnegative tensors recently. This result is a fundamental result in matrix theory and has found wide applications in ...

متن کامل

A Projected Alternating Least square Approach for Computation of Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. Methods in alternating least square (ALS) approach usually used to solve this non-convex minimization problem.  At each step of ALS algorithms two convex least square problems should be solved, which causes high com...

متن کامل

Ela a Contribution to Collatz’s Eigenvalue Inclusion Theorem for Nonnegative Irreducible Matrices∗

The matrix calculus is widely applied in various branches of mathematics and control system engineering. In this paper properties of real matrices with nonnegative elements are studied. The classical Collatz theorem is unique and immediately applicable to estimating the spectral radius of nonnegative irreducible matrices. The coherence property is identified. Then the Perron–Frobenius theorem a...

متن کامل

A contribution to Collatz's eigenvalue inclusion theorem for nonnegative irreducible matrices

The matrix calculus is widely applied in various branches of mathematics and control system engineering. In this paper properties of real matrices with nonnegative elements are studied. The classical Collatz theorem is unique and immediately applicable to estimating the spectral radius of nonnegative irreducible matrices. The coherence property is identified. Then the Perron–Frobenius theorem a...

متن کامل

Computing the Matrix Geometric Mean of Two HPD Matrices: A Stable Iterative Method

A new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for computing the geometric mean of two Hermitian positive definite matrices is constructed. Moreover, another efficient algorithm for this purpose is derived free from the computation of principal matrix...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010