A space efficient flexible pivot selection approach to evaluate determinant and inverse of a matrix.
This paper presents new simple approaches for evaluating determinant and inverse of a matrix. The choice of pivot selection has been kept arbitrary thus they reduce the error while solving an ill conditioned system. Computation of determinant of a matrix has been made more efficient by saving unnecessary data storage and also by reducing the order of the matrix at each iteration, while dictionary notation [1] has been incorporated for computing the matrix inverse thereby saving unnecessary calculations. These algorithms are highly class room oriented, easy to use and implemented by students. By taking the advantage of flexibility in pivot selection, one may easily avoid development of the fractions by most. Unlike the matrix inversion method [2] and [3], the presented algorithms obviate the use of permutations and inverse permutations.
Department of Mathematical Sciences, University of Karachi, Karachi, Pakistan.
Hafsa Athar
HA
Jafree
Department of Mathematical Sciences, University of Karachi, Karachi, Pakistan.
Muhammad
M
Imtiaz
Department of Mathematical Sciences, University of Karachi, Karachi, Pakistan.
Syed
S
Inayatullah
Department of Mathematics, Sir Syed University of Engineering and Technology, Karachi, Pakistan.
Fozia Hanif
FH
Khan
Department of Mathematics, Iqra University, Karachi, Pakistan.
Tajuddin
T
Nizami
D000465:Algorithms; D000818:Animals; D019295:Computational Biology / Q000379:methods*; D006801:Humans; D008954:Models, Biological; D016011:Normal Distribution; D015203:Reproducibility of Results; D012106:Research / Q000706:statistics & numerical data*; D013223:Statistics as Topic / Q000379:methods*