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An Toeplitz matrix may be defined as a matrix where , =, for constants , …,. The set of n × n {\displaystyle n\times n} Toeplitz matrices is a subspace of the vector space of n × n {\displaystyle n\times n} matrices (under matrix addition and scalar multiplication).
Levinson recursion or Levinson–Durbin recursion is a procedure in linear algebra to recursively calculate the solution to an equation involving a Toeplitz matrix.The algorithm runs in Θ(n 2) time, which is a strong improvement over Gauss–Jordan elimination, which runs in Θ(n 3).
1.1 Block Toeplitz Matrix Inversion. 3 comments. 1.2 One-tailed or two-tailed test of significance. 10 comments. 1.3 Simple language. 12 comments. Toggle the table of ...
This is applied, e.g., in the Kalman filter and recursive least squares methods, to replace the parametric solution, requiring inversion of a state vector sized matrix, with a condition equations based solution. In case of the Kalman filter this matrix has the dimensions of the vector of observations, i.e., as small as 1 in case only one new ...
In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. [1] [2]Intuitively, a matrix interpreted as a block matrix can be visualized as the original matrix with a collection of horizontal and vertical lines, which break it up, or partition it, into a collection of smaller matrices.
The Toeplitz Hash Algorithm describes hash functions that compute hash values through matrix multiplication of the key with a suitable Toeplitz matrix. [1] The Toeplitz Hash Algorithm is used in many network interface controllers for receive side scaling. [2] [3] As an example, with the Toeplitz matrix the key results in a hash as follows:
The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's method. In particular, if either exp {\displaystyle \exp } or log {\displaystyle \log } in the complex domain can be computed with some complexity, then that complexity is ...
Any circulant is a matrix polynomial (namely, the associated polynomial) in the cyclic permutation matrix: = + + + + = (), where is given by the companion matrix = []. The set of n × n {\displaystyle n\times n} circulant matrices forms an n {\displaystyle n} - dimensional vector space with respect to addition and scalar multiplication.