Numerical Analysis

FIRST STEPS in Numerical Analysis by
R.J.Hosking, S.Joe, D.C.Joyce, and J.C.Turner

Lectures given at Mahidol University by R. Radok during 1985-1997
using First Steps by Hosking et al. and Computational Mathematics
by B.P. Demidovich & I.A.Maron as well as other material

ERRORS

 I. INTRODUCTION
I. ERRORS 1 II. AN ALGORITHM: CONTINUED FRACTIONS
II. ERRORS 2 III. RATIONAL FUNCTIONS/
POWER SERIES EXPANSION IN CONTINUED FRACTIONS
III. ERRORS 3 IV. EVALUATION OF POLYNOMIALS
IV. FLOATING POINT ARITHMETIC V. FLOATING POINT ARITHMETIC
V. FUNCTION APPROXIMATION VI. ROOTS OF NON-LINEAR EQUATIONS

NON-LINEAR EQUATIONS

 VII. LINEAR EQUATIONS
VI. NON-LINEAR EQUATIONS 1 VIII. SPECIAL MATRICES
VII. NON-LINEAR EQUATIONS 2 IX. GAUSS ELIMINATION
VIII. NON-LINEAR EQUATIONS 3 X. MATRIX INVERSION
IX. METHOD OF SIMPLE ITERATION XI. L-U DECOMPOSITION
X. NEWTON-RAPHSON ITERATIVE METHOD XII. SHIFT OPERATORS

SYSTEMS OF EQUATIONS

 XIII. FINITE DIFFERENCES
XI. SOLUTION BY ELIMINATION XIV. INTERPOLATION
XII. ERRORS AND ILL-CONDITIONING XV. NUMERICAL INTEGRATION
XIII. THE GAUSS-SEIDEL ITERATIVE METHOD XVI PSEUDO CODE
XIV. MATRIX INVERSION  
XV. USE OF LU DECOMPOSITION  
XVI. TESTING FOR ILL-CONDITIONING  

THE EIGEN-VALUE PROBLEM

  
XVII. THE POWER METHOD  

FINITE DIFFERENCES

  
XVIII. TABLES  
XIX. FORWARD. BACKWARD AND CENTRAL DIFFERENCES  
XX. POLYNOMIALS  

INTERPOLATION

  
XXI. LINEAR AND QUADRATIC INTERPOLATION
XXII. NEWTON INTERPOLATION FORMULA		  
XXIII. LAGRANGE INTERPOLATION FORMULAE  
XXIV. DIVIDED DIFFERENCES  
XXV. INVERSE INTERPOLATION  

CURVE FITTING

  
XXVI. LEAST SQUARES  
XXVII. LEAST SQUARES AND LINEAR EQUATIONS  
XXVIII. SPLINES  

NUMERICAL DIFFERENTIATION

  
XXIX. FINITE DIFFERENCES  

NUMERICAL INTEGRATION

  
XXX. THE TRAPEZOIDAL RULE  
XXXI. SIMPSON'S RULE  
XXXII. GAUSS INTEGRATION FORMULA  

ORDINARY DIFFERENTIAL EQUATIONS

  
XXXIII. SINGLE-STEP METHODS EQUATIONS  
XXXIV. MULTI-STEP METHODS  
XXXV. HIGHER ORDER DIFFERENTIAL