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Contents
l. Introduction
1
2. Some Fundamental Numerical Methods
2.1. Complex Four Functions, 7
2.2. Linear Systems of Equations, 8
2.2.1. The Gauss-Jordan Elimination Method, 9
2.2.2. Linear Equations With Complex Coefficients, I I
2.2.3. Linear Equations Summary, 12
2.3. Romberg Integration, 13
2.3.1 Trapezoidal Integration, ]4
2.3.2. Repeated Linear Interpolation and the Limit, 15
2.3.3. Romberg Integration Program, 17
2.3.4. Simpson's Integration Rule, 18
2.3.5. Summary of Integration, 18
2.4. Polynomial Minimax Approximation of Piecewise Linear Functions, 19
2.4.1. Chebyshev Functions of the First Kind, 19
2.4.2. Chebyshev Expansions, 20
2.4.3. Expansion Coefficients for Piecewise Linear Functions, 21
2.4.4. A Minimax Approximation Program, 22
2.4.5. Piecewise Linear Function Approximation Summary, 24
2.5. Rational Polynomial LSE Approximation of Complex Functions, 24
2.5.1. The Basis of Levy's Complex Curve-Fining Method, 26
2.5.2. Complex Curve·Fitting Procedure, 27
2.5.3. Summary of Complex Curve·Fitting by Rational
Polynomials, 30
Problems, 30
7
3. Some Tools and Examples of Filter Synthesis
3. J. Complex Zeros of Complex Polynomials, 34
3.1.1. Moore's Root Finder, 36
34
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