English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The article discusses the matrices of the three forms whose inversions are:tridiagonal matrix, banded matrix or block-tridiagonal matrix and theirrelationships with the covariance matrices of measurements of ordinary (simple)Markov Random Processes (MRP), multiconnected MRP and vector MRP respectively.Such covariance matrices are frequently occurring in the problems of optimalfiltering, extrapolation and interpolation of MRP and Markov Random Fields(MRF). It is shown, that the structure of these three forms of matrices has thesame form, but the matrix elements in the first case are scalar quantities; inthe second case matrix elements representing a product of vectors of dimensionm; and in the third case, the off-diagonal elements are the product of matricesand vectors of dimension m. The properties of such matrices were investigatedand a simple formulas of their inversion was founded. Also computationalefficiency in the storage and inverse of such matrices have been considered. Toillustrate the acquired results an example of the covariance matrix inversionsof two-dimensional MRP is given.

Matrices Whose Inversions are Tridiagonal, Band or Block-Tridiagonal and  Their Relationship with the Covariance Matrices of a Random Markov Processes  (Fields)