Bivariate Matrix Functions

نویسندگان

  • DANIEL KRESSNER
  • I. M. JAIMOUKHA
چکیده

A definition of bivariate matrix functions is introduced and some theoretical as well as algorithmic aspects are analyzed. It is shown that our framework naturally extends the usual notion of (univariate) matrix functions and allows to unify existing results on linear matrix equations and derivatives of matrix functions. Mathematics subject classification (2010): 15A16, 15A24, 15A69.

برای دانلود رایگان 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

SOLVING NONLINEAR TWO-DIMENSIONAL VOLTERRA INTEGRAL EQUATIONS OF THE FIRST-KIND USING BIVARIATE SHIFTED LEGENDRE FUNCTIONS

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...

متن کامل

ON THE POWER FUNCTION OF THE LRT AGAINST ONE-SIDED AND TWO-SIDED ALTERNATIVES IN BIVARIATE NORMAL DISTRIBUTION

This paper addresses the problem of testing simple hypotheses about the mean of a bivariate normal distribution with identity covariance matrix against restricted alternatives. The LRTs and their power functions for such types of hypotheses are derived. Furthermore, through some elementary calculus, it is shown that the power function of the LRT satisfies certain monotonicity and symmetry p...

متن کامل

A Krylov subspace method for the approximation of bivariate matrix functions

Bivariate matrix functions provide a unified framework for various tasks in numerical linear algebra, including the solution of linear matrix equations and the application of the Fréchet derivative. In this work, we propose a novel tensorized Krylov subspace method for approximating such bivariate matrix functions and analyze its convergence. While this method is already known for some instance...

متن کامل

Parameterization of Bivariate Nonseparable Orthogonal Symmetric Scaling Functions with Short Support

Let I be the 2 × 2 identity matrix, and M a 2 × 2 dilation matrix with M = 2I . First, we present the correlation of the scaling functions with dilation matrix M and 2I . Then by relating the properties of scaling functions with dilation matrix 2I to the properties of scaling functions with dilation matrix M , we give a parameterization of a class of bivariate nonseparable orthogonal symmetric ...

متن کامل

An Extension of Warnaar’s Matrix Inversion

We present a necessary and sufficient condition for two matrices given by two bivariate functions to be inverse to each other with certainty in the cases of Krattenthaler formula and Warnaar’s elliptic matrix inversion. Immediate consequences of our result are some known functions and a constructive approach to derive new matrix inversions from known ones.

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010