Inverse M-matrix And Its Complete Problem And Non-negative Matrix

Special matrices play an important role in matrix analysis and matrixcomputation and have wide applications in computational mathematics, economics,physics, biology, applied mathematics and etc. Great progress obtained in theresearches on special matrices will give improvements in computationalmathematics. This dissertation presents inverse M-matrices and M-matrix, theproperties and completion of inverse M-matrices. And the closure property of inverseM-matrices under Hadamard product are analyzed, the properties of generalizedPerron complement of inverse M-matrices, inequality of Fan product of H-matricesand Perron root estimation of nonnegative matrix are studied.This dissertation is divided into five chapters: Chapter one is devoted tointroducing the background and some related definition and nation.In Chapter 2 wediscuss the properties of inverse M-matrices. Chapter 3 considers completion ofinverse M-matrices and its closure property under Hadamard product. In Chapter 4we obtained the properties of the generalized Perron complement of inverseM-matrices and inequality of Fan product of H-matrices. Chapter 5, we get shaperupper and lower bounds of perron root of the matrix by the perron root of A2 undersome conditions. Some examples are given to show the new estimation method iseffective.