Computing the Logarithm of a Symmetric Positive Deenite Matrix

نویسنده

  • Ya Yan Lu
چکیده

A numerical method for computing the logarithm of a symmetric positive dee-nite matrix is developed in this paper. It is based on reducing the original matrix to a tridiagonal matrix by orthogonal similarity transformations and applying Pad e approximations to the logarithm of the tridiagonal matrix. Theoretical studies and numerical experiments indicate that the method is quite eecient when the matrix is not very ill-conditioned.

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

Symmetric Schemes for Computing the Minimum Eigenvalue of a Symmetric Toeplitz Matrix

In 8] and 9] W. Mackens and the present author presented two generalizations of a method of Cybenko and Van Loan 4] for computing the smallest eigenvalue of a symmetric, positive deenite Toeplitz matrix. Taking advantage of the symmetry or skew symmetry of the corresponding eigenvector both methods are improved considerably.

متن کامل

Similarity and other spectral relations for symmetric cones

A one{to{one relation is established between the nonnegative spectral values of a vector in a primitive symmetric cone and the eigenvalues of its quadratic representation. This result is then exploited to derive similarity relations for vectors with respect to a general symmetric cone. For two positive deenite matrices X and Y , the square of the spectral geometric mean is similar to the matrix...

متن کامل

A Projection Method for Computing the MinimumEigenvalue of a Symmetric Positive De nite Toeplitz

A projection method for computing the minimal eigenvalue of a symmetric and positive deenite Toeplitz matrix is presented. It generalizes and accelerates the algorithm considered in 12]. Global and cubic convergence is proved. Randomly generated test problems up to dimension 1024 demonstrate the methods good global behaviour.

متن کامل

A Projection Method for Computing the Minimum Eigenvalue of a Symmetric Positive De nite Toeplitz Matrix

A projection method for computing the minimal eigenvalue of a symmetric and positive deenite Toeplitz matrix is presented. It generalizes and accelerates the algorithm considered in 12]. Global and cubic convergence is proved. Randomly generated test problems up to dimension 1024 demonstrate the methods good global behaviour.

متن کامل

A Necessary and Sufficient Symbolic Condition for the Existence of Incomplete Cholesky Factorization

This paper presents a suucient condition on sparsity patterns for the existence of the incomplete Cholesky factorization. Given the sparsity pattern P(A) of a matrix A, and a target sparsity pattern P satisfying the condition, incomplete Cholesky factorization successfully completes for all symmetric positive deenite matrices with the same pattern P(A). This condition is also necessary in the s...

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 2007