In a multiple linear regression model, there are instances where one has to update the regression parameters. In such models as new data become available, by adding one row to the design matrix, the least-squares estimates for the parameters must be updated to reflect the impact of the new data. We will modify two existing methods of calculating regression coefficients in multiple linear regres...

We evaluate and compare the storage efficiency of different sparse matrix storage formats as index structure for text collection and their corresponding sparse matrixvector multiplication algorithm to perform query processing in information retrieval (IR) application. We show the results of our implementations for several sparse matrix algorithms such as Coordinate Storage (COO), Compressed Spa...

Exercise 7. Let A be an n × n matrix such that the sum of every row is 0 and the sum of every column is 0. Let Aij be the (n − 1) × (n − 1) matrix obtained by removing row i and column j from A. Prove: det(Aij) = (−1) det(A11). (Note that this result applies in particular to the Laplacian L: the determinant of the reduced Laplacian, obtained by removing the i-th row and the i-th column from L, ...

We give simple necessary and sufficient conditions for the existence of a zero-one matrix with given row and column sums and at most one structural zero in each row and column. © 2006 Elsevier B.V. All rights reserved.

An alternating sign matrix [1] is a generalization of a permutation matrix. It consists of a matrix whose entries are 1, −1, and 0, and it satisfies the condition that in every row and column, the 1’s and −1’s alternate (possibly with 0’s in between) and the sum of the entries in every row or column is equal to 1 (so the permutation matrices are one type of these, in which there are no −1’s). F...

The present paper discusses the implementations of sparse matrix-vector products, which are crucial for high performance solutions of large-scale linear equations, on a PC-Cluster. Three storage formats for sparse matrices compressed row storage, block compressed row storage and sparse block compressed row storage are evaluated. Although using BCRS format reduces the execution time but the impr...

We consider designing a sparse sensing matrix which contains few non-zero entries per row for compressive sensing (CS) systems. By unifying the previous approaches for optimizing sensing matrices based on minimizing the mutual coherence, we propose a general framework for designing a sparse sensing matrix that minimizes the mutual coherence of the equivalent dictionary and is robust to sparse r...

In this paper a novel approach for matrix manipulation and indexing is proposed .Here the elements in a row of matrix are designated by numeric value called ‘permutation index’ followed by the elements of the row being randomised. This is done for all the rows of the matrix and in the end the set of permutation indices are put in the parent matrix and random locations depending on a pre decided...

We determine analytically the modulus of the second eigenvalue for the web hyperlink matrix used by Google for computing PageRank. Specifically, we prove the following statement: “For any matrix , where is an row-stochastic matrix, is a nonnegative rank-one row-stochastic matrix, and ! " , the second eigenvalue of has modulus # $&%'#( ) . Furthermore, if has at least two irreducible closed subs...