On the Fréchet derivative of matrix functions

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

The operational matrix of fractional derivative of the fractional-order Chebyshev functions and its applications

In this paper, we introduce a family of fractional-order Chebyshev functions based on the classical Chebyshev polynomials. We calculate and derive the operational matrix of derivative of fractional order $gamma$ in the Caputo sense using the fractional-order Chebyshev functions. This matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

متن کامل

The Fréchet Derivative of the Polar Decomposition

We derive iterative methods for computing the Fréchet derivative of the map which 6 sends a full-rank matrix A to the factor U in its polar decomposition A = UH, where U has 7 orthonormal columns and H is Hermitian positive definite. The methods apply to square matrices 8 as well as rectangular matrices having more rows than columns. Our derivation relies on a novel 9 identity that relates the ...

متن کامل

Iterative Computation of the Fréchet Derivative Of

We derive iterative methods for computing the Fréchet derivative of the map which 4 sends a full-rank matrix A to the factor U in its polar decomposition A = UH, where U has 5 orthonormal columns and H is Hermitian positive definite. The methods apply to square matrices 6 as well as rectangular matrices having more rows than columns. Our derivation relies on a novel 7 identity that relates the ...

متن کامل

Computing the Fréchet Derivative of the Matrix Logarithm and Estimating the Condition Number

The most popular method for computing the matrix logarithm is the inverse scaling and squaring method, which is the basis of the recent algorithm of [A. H. Al-Mohy and N. J. Higham, Improved inverse scaling and squaring algorithms for the matrix logarithm, SIAM J. Sci. Comput., 34 (2012), pp. C152–C169]. We show that by differentiating the latter algorithm a backward stable algorithm for comput...

متن کامل

Estimating the Condition Number of the Fréchet Derivative of a Matrix Function

ESTIMATING THE CONDITION NUMBER OF THE FRÉCHET DERIVATIVE OF A MATRIX FUNCTION∗ NICHOLAS J. HIGHAM† AND SAMUEL D. RELTON† Abstract. The Fréchet derivative Lf of a matrix function f : C n×n → Cn×n is used in a variety of applications and several algorithms are available for computing it. We define a condition number for the Fréchet derivative and derive upper and lower bounds for it that differ ...

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: Linear Algebra and its Applications

سال: 1987

ISSN: 0024-3795

DOI: 10.1016/0024-3795(87)90062-0