tailieunhanh - Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 89

Tham khảo tài liệu 'lập trình c# all chap "numerical recipes in c" part 89', công nghệ thông tin phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 36 Chapter2. Solution ofLinearAlgebraic Equations Coleman . and Van Loan C. 1988 HandbookforMatrix Computations Philadelphia . . Forsythe . and Moler . 1967 Computer Solution of Linear Algebraic Systems Englewood Cliffs NJ Prentice-Hall . Wilkinson . and Reinsch C. 1971 Linear Algebra vol. II of Handbook for Automatic Computation New York Springer-Verlag . Westlake . 1968 A Handbook ofNumerical Matrix Inversion and Solution ofLinear Equations New York Wiley . Johnson . and Riess . 1982 Numerical Analysis 2nd ed. Reading MA Addison-Wesley Chapter 2. Ralston A. and Rabinowitz P. 1978 A First Course in Numerical Analysis 2nd ed. New York McGraw-Hill Chapter 9. Gauss-Jordan Elimination For inverting a matrix Gauss-Jordan elimination is about as efficient as any other method. For solving sets of linear equations Gauss-Jordan elimination produces both the solution of the equations for one or more right-hand side vectors b and also the matrix inverse A-1. However its principal weaknesses are i that it requires all the right-hand sides to be stored and manipulated at the same time and ii that when the inverse matrix is not desired Gauss-Jordan is three times slower than the best alternative technique for solving a single linear set . The method s principal strength is that it is as stable as any other direct method perhaps even a bit more stable when full pivoting is used see below . If you come along later with an additional right-hand side vector you can multiply it by the inverse matrix of course. This does give an answer but one that is quite susceptible to roundoff error not nearly as good as if the new vector had been included with the set of right-hand side vectors in the first instance. For these reasons Gauss-Jordan elimination should usually not be your method of first choice either for solving linear equations or for matrix inversion. The decomposition methods in are better. Why do we give you Gauss-Jordan at all Because .

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