The article discusses the matrices of the 1 n A , m n A , m N A forms, whose inversions are: tridiagonal matrix 1 n A (ndimension of the matrix), banded matrix m n A (m -the half-width band of the matrix) or block-tridiagonal matrix m N A (N=n x mfull dimension of the block matrix; m -the dimension of the blocks) and their relationships with the covariance matrices of measurements with ordinary (simple) Markov Random Processes (MRP), multiconnected MRP and vector MRP respectively. Such covariance matrices are frequently occurring in the problems of optimal filtering, extrapolation and interpolation of MRP and Markov Random Fields (MRF). It is shown, that the structure of the matrix 1 n A , m n A , m N A , has the same form, but the matrix elements in the first case are scalar quantities; in the second case matrix elements representing a product of vectors of dimension m; and in the third case, the off-diagonal elements are the product of matrices and vectors of dimension m. The properties of such matrices were investigated and a simple formulas of their inversion was founded. Also computational efficiency in the storage and inverse of such matrices have been considered. To illustrate the acquired results an example of the covariance matrix inversions of two-dimensional MRP is given. Index Terms-Best Linear Unbiased Estimates (BLUE), Markov process in the wide sense, simple (ordinary connected) Markov process, multiply connected (m-connected) Markov process, vector (m-dimensional) Markov process, Random field filtering and parametric identification, Tridiagonal Matrices, Banded Matrices and Block-Tridiagonal matrices.
Many examinations with thousands of participating students are organized worldwide every year. Usually, this large number of students sit the exams simultaneously and answer almost the same set of questions. This method of learning assessment requires tremendous effort and resources to prepare the venues, print question books and organize the whole process. Additional restrictions and obstacles may appear in conditions similar to those during the COVID-19 pandemic. One way to obviate the necessity of having all the students take an exam during the same period of time is to use a computer-assisted assessment with random item selection, so that every student receives an individual set of questions. The objective of this study is to investigate students’ perceptions of using random item selection from item banks in order to apply this method in large-scale assessments. An analysis of the responses of more than 1000 surveyed students revealed that most of them agree or completely agree with using the proposed method of assessment. The students from natural science departments showed more tolerance of this method of assessment compared with students from other groups. Based on the findings of this study, the authors concluded that higher-education institutions could benefit from implementing the abovementioned assessment method.
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