Path norms on a matrix

Soft Computing - Tập 27 - Trang 6939-6959 - 2023
Varsha1, S. Aishwarya1, Syam Prasad Kuncham1, Babushri Srinivas Kedukodi1
1Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education(MAHE), Manipal, India

Tóm tắt

We define row path norm and column path norm of a matrix and relate path norms with other standard matrix norms. A row (resp. column) path norm gives a path that maximizes relative row (resp. column) distances starting from the first row (resp. column). The comparison takes place from the last row (resp. column) to the first row (resp. column), tracing the path. We categorize different versions of path norms and provide algorithms to compute them. We show that brute-force methods to compute path norms have exponential running time. We give dynamic programming algorithms, which, in contrast, take quadratic running time for computing the path norms. We define path norms on Church numerals and Church pairs. Finally, we present applications of path norms in computing condition number, and ordering the solutions of magic squares and Latin squares

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