HP HP-15C - Contents

Contents 3
Multivalued Functions 69
Using | SOLVE | and |7T| in Complex Mode 73
Acuracy in Complex Mode 73
Applications 76
Storing and Recalling Complex Numbers Using a Matrix 76
Calculating the /?th Roots of a Complex Number 78
Solving an Equation for Its Complex Roots 80
Contour Integrals 85
Complex Potentials 89
Section 4: Using Matrix Operations 96
Understanding the LU Decomposition 96
Ill-Conditioned Matrices and the Condition Number 98
The Accuracy of Numerical Solutions to Linear Systems 103
Making Difficult Equations Easier 104
Scaling 104
Preconditioning 1 07
Least-Squares Calculations 110
Normal Equations 110
Orthogonal Factorization 113
Singular and Nearly Singular Matrices 117
Applications 119
Constructing an Identity Matrix 119
One-Step Residual Correction 119
Solving a System of Nonlinear Equations 122
Solving a Large System of Complex Equations 128
Least-Squares Using Normal Equations 131
Least-Squares Using Successive Rows 140
Eigenvalues of a Symmetric Real Matrix 148
Eigenvectors of a Symmetric Real Matrix 154
Optimization 1 60
Appendix: Accuracy of Numerical Calculations 172
Misconceptions About Errors 172
A Hierarchy of Errors 178
Level 0: No Error 178
Level oo: Overflow/Underflow 179
Level 1: Correctly Rounded, or Nearly So 179
Level 1 C: Complex Level 1 183
Level 2: Correctly Rounded for Possibly Perturbed Input 1 84
Trigonometric Functions of Real Radian Angles 184
Backward Error Analysis 1 87