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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).
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).
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 ...
Versions exist for both C++ and the Java programming language. The C++ version uses the Template Numerical Toolkit for lower-level operations. The Java version provides the lower-level operations itself.
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:
An circulant matrix takes the form = [] or the transpose of this form (by choice of notation). If each is a square matrix, then the matrix is called a block-circulant matrix.. A circulant matrix is fully specified by one vector, , which appears as the first column (or row) of .
Examples of such matrices commonly arise from the discretization of 1D Poisson equation and natural cubic spline interpolation. Thomas' algorithm is not stable in general, but is so in several special cases, such as when the matrix is diagonally dominant (either by rows or columns) or symmetric positive definite ; [ 1 ] [ 2 ] for a more precise ...
The first widely used algorithm for solving this problem is an active-set method published by Lawson and Hanson in their 1974 book Solving Least Squares Problems. [5]: 291 In pseudocode, this algorithm looks as follows: [1] [2]