Solving Sylvester equation with complex symmetric semi-definite positive coefficient matrices
نویسندگان
چکیده
Combination of real and imaginary parts (CRI) works well for solving complex symmetric linear systems. This paper develops a generalization CRI method to determine the solution Sylvester matrix equation. We show that this, regardless condition, converges At end we test new scheme by numerical example.
منابع مشابه
DDtBe for Band Symmetric Positive Definite Matrices
We present a new parallel factorization for band symmetric positive definite (s.p.d) matrices and show some of its applications. Let A be a band s.p.d matrix of order n and half bandwidth m. We show how to factor A as A =DDt Be using approximately 4nm2 jp parallel operations where p =21: is the number of processors. Having this factorization, we improve the time to solve Ax = b by a factor of m...
متن کاملProduct of three positive semi-definite matrices
In [2], the author showed that a square matrix with nonnegative determinant can always be written as the product of five or fewer positive semi-definite matrices. This is an extension to the result in [1] asserting that every matrix with positive determinant is the product of five or fewer positive definite matrices. Analogous to the analysis in [1], the author of [2] studied those matrices whi...
متن کاملSemi-supervised Multi-label Learning by Solving a Sylvester Equation
Multi-label learning refers to the problems where an instance can be assigned to more than one category. In this paper, we present a novel Semi-supervised algorithm for Multi-label learning by solving a Sylvester Equation (SMSE). Two graphs are first constructed on instance level and category level respectively. For instance level, a graph is defined based on both labeled and unlabeled instance...
متن کاملFactorizing complex symmetric matrices with positive definite real and imaginary parts
Complex symmetric matrices whose real and imaginary parts are positive definite are shown to have a growth factor bounded by 2 for LU factorization. This result adds to the classes of matrix for which it is known to be safe not to pivot in LU factorization. Block LDLT factorization with the pivoting strategy of Bunch and Kaufman is also considered, and it is shown that for such matrices only 1×...
متن کاملEstimation of symmetric positive-definite matrices from imperfect measurements
In a number of contexts relevant to control problems, including estimation of robot dynamics, covariance, and smart structure mass and stiffness matrices, we need to solve an over-determined set of linear equations AX ≈ B with the constraint that the matrix X be symmetric and positive definite. In the classical least squares method the measurements of A are assumed to be free of error, hence, a...
متن کاملذخیره 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: Filomat
سال: 2022
ISSN: ['2406-0933', '0354-5180']
DOI: https://doi.org/10.2298/fil2205743s