tailieunhanh - numerical mathematics and scientific computation volume 1 Episode 1

Tham khảo tài liệu 'numerical mathematics and scientific computation volume 1 episode 1', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Contents 1 Principles of Numerical Calculations 1 Introduction. 1 Common Ideas and Concepts. 2 Iteration . 2 Linearization and Extrapolation. 5 Finite Difference Approximations. 9 Review Questions. 12 Problems and Computer Exercises. 12 Numerical Algorithms. 13 Recurrence Relations . 13 Divide and Conquer Strategy. 16 Approximation of Functions. 17 Solving Linear System of Equations. 20 Review Questions. 29 Problems and Computer Exercises. 29 Numerical Solution of Differential Equations. 32 Euler s Method. 32 An Introductory Example. 33 A Second Order Method. 36 Review Questions. 40 Problems. 40 Computer Exercises. 41 Monte Carlo Methods. 41 Origin of Monte Carlo Methods. 41 Random and Pseudo-Random Numbers. 43 Reduction of Variance. 47 Review Questions. 50 Problems. 50 Linear Algebra and Matrix Computations . 51 Linear Vector Spaces. 51 Matrix and Vector Algebra. 52 Partitioning and Block Matrices. 57 Inner Products Orthogonality and Projections . 59 Linear Least Squares Problems. 61 i ii Contents Similarity Transformations and Eigenvalues. 63 The Singular Value Decomposition. 65 Norms of Vectors and Matrices. 67 Review Questions. 70 Problems. 70 2 How to Obtain and Estimate Accuracy 75 Basic Concepts in Error Estimation. 75 Sources of Error. 75 Absolute and Relative Errors. 77 Rounding and Chopping. 79 Review Questions. 81 Computer Number Systems . 81 The Position System. 81 Fixed and Floating Point Representation. 83 IEEE Floating Point Standard. 86 Elementary Functions. 90 Multiple Precision Arithmetic. 91 Review Questions. 91 Problems. 91 Accuracy and Rounding Errors . 92 Floating Point Arithmetic. 92 Basic Results. 97 Compensated Summation. 99 Standard Avoiding Cancellation of .