Some Iteration Methods for Solving Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory

一些迭代方法解運輸理論的非線性黎卡迪方程式

賴金君(Chin-Chun Lai)

指導教授 ： 林文偉

國立清華大學/理學院/數學系/碩士(2009年)

摘要

We consider a nonsymmetric algebraic Riccati equation arising in transport theory. The four coefficient matrices form this equation is M-matrix, it can be determined that equation existence nonnegative solutions. We propose the new simple iterative method and Newton nonlinear black Jacobi to solve the vector equation. The convergence theorem about new simple iterative show that the sequence of vectors is monotonically increasing and converges to
the minimal nonnegative solution of vector equation. Numerical experiments show that the new simple iterative is more efficient than simple iterative.

關鍵字

Hamiltonian ； minimal nonnegative solution ； M-matrix ； monotone convergence ； Newton method ； nonsymmetric algebraic Riccati equation ； simple iterative method ； transport theory

參考文獻

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