TY - JOUR
T1 - Path norms on a matrix
AU - Varsha, null
AU - Aishwarya, S.
AU - Kuncham, Syam Prasad
AU - Kedukodi, Babushri Srinivas
N1 - Funding Information:
The authors thank the reviewers and the editor for their valuable comments and suggestions. The authors acknowledge Manipal Institute of Technology, Manipal Academy of Higher Education for the encouragement. The first and second authors acknowledge Manipal Academy of Higher Education for Dr TMA Pai PhD scholarship.
Publisher Copyright:
© 2023, The Author(s).
PY - 2023/6
Y1 - 2023/6
N2 - 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.
AB - 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.
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U2 - 10.1007/s00500-023-07910-w
DO - 10.1007/s00500-023-07910-w
M3 - Article
AN - SCOPUS:85153351056
SN - 1432-7643
VL - 27
SP - 6939
EP - 6959
JO - Soft Computing
JF - Soft Computing
IS - 11
ER -