Some Matrix Iterations for Computing Matrix Sign Function
نویسندگان
چکیده
منابع مشابه
Computing Fundamental Matrix Decompositions Accurately via the Matrix Sign Function in Two Iterations: The Power of Zolotarev's Functions
The symmetric eigenvalue decomposition and the singular value decomposition (SVD) are fundamental matrix decompositions with many applications. Conventional algorithms for computing these decompositions are suboptimal in view of recent trends in computer architectures, which require minimizing communication together with arithmetic costs. Spectral divideand-conquer algorithms, which recursively...
متن کاملThe Padé iterations for the matrix sign function and their reciprocals are optimal
It is proved that among the rational iterations locally converging with order s > 1 to the sign function, the Padé iterations and their reciprocals are the unique rationals with the lowest sum of the degrees of numerator and denominator.
متن کاملSome Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations
An application of iterative methods for computing the Moore–Penrose inverse in balancing chemical equations is considered. With the aim to illustrate proposed algorithms, an improved high order hyper-power matrix iterative method for computing generalized inverses is introduced and applied. The improvements of the hyper-power iterative scheme are based on its proper factorization, as well as on...
متن کاملComputing a Matrix Function for Exponential Integrators
An efficient numerical method is developed for evaluating φ(A), where A is a symmetric matrix and φ is the function defined by φ(x) = (ex − 1)/x = 1+ x/2 + x2/6+ .... This matrix function is useful in the so-called exponential integrators for differential equations. In particular, it is related to the exact solution of the ODE system dy/dt = Ay + b, where A and b are t-independent. Our method a...
متن کاملA modified matrix sign function method for projected Lyapunov equations
In this paper we discuss the numerical solution of projected generalized Lyapunov equations using the matrix sign function method. Such equations arise in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. It is known that the matrix sign function method applied to a matrix pencil λE−A converges if and only if λE−A is of index ...
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: Journal of Applied Mathematics
سال: 2014
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2014/425654