Numerical Methods: Problems and SolutionsIs An Outline Series Containing Brief Text Of Numerical Solution Of Transcendental And Polynomial Equations, System Of Linear Algebraic Equations And Eigenvalue Problems, Interpolation And Approximation, Differentiation And Integration, Ordinary Differential Equations And Complete Solutions To About 300 Problems. Most Of These Problems Are Given As Unsolved Problems In The Authors Earlier Book. User Friendly Turbo Pascal Programs For Commonly Used Numerical Methods Are Given In The Appendix. This Book Can Be Used As A Text/Help Book Both By Teachers And Students. |
Contents
Section 1 | 4 |
Section 2 | 5 |
Section 3 | 6 |
Section 4 | 7 |
Section 5 | 8 |
Section 6 | 11 |
Section 7 | 18 |
Section 8 | 22 |
Section 14 | 44 |
Section 15 | 47 |
Section 16 | 48 |
Section 17 | 54 |
Section 18 | 55 |
Section 19 | 56 |
Section 20 | 58 |
Section 21 | 61 |
Section 9 | 28 |
Section 10 | 31 |
Section 11 | 32 |
Section 12 | 35 |
Section 13 | 41 |
Section 22 | 62 |
Section 23 | 63 |
Section 24 | 65 |
Section 25 | 66 |
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Common terms and phrases
Aitken 2-process b₁ b₁x Bairstow's method bisection method c₁ Chebyshev method coefficients complex roots correct to three deflated polynomial determine double root En+1 equation f error equation evaluation per iteration exact root F G H f x₁ f xp f(xk f(xn f₁ fk fk function given equation h₁ h₂ Hence initial approximation interval iterates x1 iteration formula iteration method iteration scheme Jacobian matrix multiple root Newton-Raphson method 1.9 nn+1 obtain the sequence P₁ positive root rate of convergence real roots Regula-Falsi method root correct root lies root of f Secant method Second iteration sequence of iterates simple root smallest positive root Starting with x0 Sturm sequence Substituting x₁ Sweden synthetic division method system of equations third order method three decimal places Xk fk Xk+1 Xn+1 Y₁ ε₁ εο επ ερ Уп Уп+1