Sentence examples for matrix sign function from inspiring English sources
This paper proposes a tractable iterative scheme for computing parameter-dependent matrix sign function.
We compute the spectral projector by constructing the matrix sign function through a simple polynomial recursion.
We describe a hybrid Lyapunov solver based on the matrix sign function, where the intensive parts of the computation are accelerated using a graphics processor (GPU) while executing the remaining operations on a general-purpose multi-core processor (CPU).
The other methodology comes from the iterative method, for example, it is referred to as Newton's method [6], matrix sign function method [19], disk function method [20], and structured doubling algorithms [21, 22] and references therein.
These integral formulas reveal that any property or iterative method involving the matrix sign function can be transformed into one for the polar decomposition by replacing (A^{2}) via (A^A), and vice versa.
Drawing the attraction basins [15] of (10) for finding the solution of the polynomial equation (u^{2}-1=0) in the complex plane reveals that the application of (9) for finding matrix sign function and consequently the unitary polar factor has global convergence.
Following this algorithm, the matrix A is quantized by a sign function because A T in the block Newton method corresponds to the input signal in the conventional LMS algorithm.
The sign function S is defined as: And a matrix of leaping factors β is defined as a matrix form: Because β is only meaningful in two consecutive stages, the β matrix is much like a diagonal matrix.
For small dense problems one could employ the sign function method, [29, 30] but this would require storing full dense inverses of matrices of the given class, which is certainly not possible in the described acoustic field problems.
sgn denotes sign function.
