TAILIEUCHUNG - Ebook Applied numerical methods with MATLAB for engineers and scientists: Part 2

(BQ) Part 2 book "Applied numerical methods with MATLAB for engineers and scientists" has contents: Matrix inverse and condition, matrix inverse and condition, eigenvalues, linear regression, polynomial interpolation, numerical integration formulas,.and other contents. | 11 Matrix Inverse and Condition CHAPTER OBJECTIVES The primary objective of this chapter is to show how to compute the matrix inverse and to illustrate how it can be used to analyze complex linear systems that occur in engineering and science. In addition, a method to assess a matrix solution’s sensitivity to roundoff error is described. Specific objectives and topics covered are • • • • • Knowing how to determine the matrix inverse in an efficient manner based on LU factorization. Understanding how the matrix inverse can be used to assess stimulus-response characteristics of engineering systems. Understanding the meaning of matrix and vector norms and how they are computed. Knowing how to use norms to compute the matrix condition number. Understanding how the magnitude of the condition number can be used to estimate the precision of solutions of linear algebraic equations. THE MATRIX INVERSE In our discussion of matrix operations (Section ), we introduced the notion that if a matrix [A] is square, there is another matrix [A]−1 , called the inverse of [A], for which [A][A]−1 = [A]−1 [A] = [I ] () Now we will focus on how the inverse can be computed numerically. Then we will explore how it can be used for engineering analysis. Calculating the Inverse The inverse can be computed in a column-by-column fashion by generating solutions with unit vectors as the right-hand-side constants. For example, if the right-hand-side constant 268 12/17/10 8:10 AM Page 269 THE MATRIX INVERSE 269 has a 1 in the first position and zeros elsewhere, 1 {b} = 0 () 0 the resulting solution will be the first column of the matrix inverse. Similarly, if a unit vector with a 1 at the second row is used 0 {b} = 1 () 0 the result will be the second column of the matrix inverse. The best way to implement such a calculation is with LU factorization. Recall that one of the great strengths of LU factorization is that it .

• Cơ khí - Chế tạo máy
• Applied numerical methods
• MATLAB for engineers and scientists
• Matrix inverse
• Linear regression
• Polynomial interpolation
• Numerical integration formulas
• Mathematical modeling
• Numerical methods
• Problem solving
• Matlab fundamentals
• Programming with matlab
• Bracketing methods
• Fourier analysis
• Numerical differentiation
• Boundary value problems
• Truncation errors
• Ứng dụng phương pháp tính số
• Phương pháp tính số
• Ngôn ngữ lập trình Fortran
• Fortran cơ sở
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• Phương trình đại số phi tuyến
• Phương pháp khoanh vùng
• Phương pháp phi đạo hàm
• Phương pháp tính trực tiếp
• Phương pháp lặp
• Phương pháp khử Gaussian
• Phương pháp bình phương tối thiểu
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• Bài toán giá trị đầu
• Vietnam Journal of Mechanics
• Combination of collocation and factorization methods applied
• Numerical solutions of bubble inside drop system dynamics
• Bubble inside drop system dynamics
• Drop system dynamics
• A guide to MATLAB
• Beginners and experienced users
• Developing your MATLAB skills
• MATLA bandthe internet
• MATLAB help on the internet
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