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Transactions: WSEAS TRANSACTIONS ON MATHEMATICS
Transactions ID Number: 53-811
Full Name: Yuanyuan Liu
Position: Student
Age: ON
Sex: Female
Address: Tianjin Polytechnic University Tianjin 300160
Country: CHINA
Tel: 13820667551
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E-mail address: angelpeople@126.com
Other E-mails: angel__people2163.com
Title of the Paper: the ill-conditioned matrix and ill-conditioned linear system of algebraic equations
Authors as they appear in the Paper: Yuanyuan Liu,Junqing Wang,Hongjie Liu
Email addresses of all the authors: angelpeople@126.com,tjgdwjq@sina.com,liuhongjie198891@yahoo.cn
Number of paper pages: 11
Abstract: We know that matrix is a table of m rows and n columns, there are many special matrices such as Gram matrix, controllability matrix, nonnegative matrix, band matrix, shift matrix, geometric matrix, harmonic matrix, ill-conditioned matrix and so on . In this article the ill-conditioned matrices will be introduced. They have the property that when there is a small change, the computer results will be changed seriously, especially when it comes to the solution of linear system of algebraic equations. The ill-condition of a matrix can be measured by the condition number of , it can be notated by , and it is equal to the multiplication of the norm of A and the norm of the inverse of . This article includes six sections, the condition number of matrices will be introduced; the ill-conditioned matrices will be defined; the display of ill-conditioned matrices on linear system of algebraic equations will also be discussed; the existence methods of solving the linear sys!
tem of algebraic equations will be compared; the improved singular value decomposition method and the conclusion in the final of this article.
Keywords: Ill-conditioned matrix; Condition number; Linear system of algebraic of equations
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