Chapter 3 Interpolation and Polynomial Approximation Numerical Analysis

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Chapter 3 Interpolation and Polynomial Approximation Numerical Analysis

Chapter 3 Interpolation and Polynomial Approximation Numerical Analysis

Theory of Weierstrass

Theory of Weierstrass

Interpolation: Overview

Interpolation: Overview

Interpolation: Overview

Interpolation: Overview

Interpolation: Overview

Interpolation: Overview

Lagrange Polynomial

Lagrange Polynomial

Lagrange Polynomial

Lagrange Polynomial

Lagrange Polynomial

Lagrange Polynomial

Lagrange Polynomial

Lagrange Polynomial

Lagrange Polynomial: Example

Lagrange Polynomial: Example

Lagrange Polynomial: Example

Lagrange Polynomial: Example

Lagrange Polynomial: Example

Lagrange Polynomial: Example

Divided Difference

Divided Difference

Divided Difference

Divided Difference

Divided Difference

Divided Difference

Newton Divided Difference: Example

Newton Divided Difference: Example

Newton Divided Difference: Example xi 1. 0 f(xi)=f[xi] 0. 7651977 1. 3 0. 6200860

Newton Divided Difference: Example xi 1. 0 f(xi)=f[xi] 0. 7651977 1. 3 0. 6200860 1. 6 0. 4554022 1. 9 0. 2818186 2. 2 0. 1103623 1 st Divided Diff 2 nd Divided Diff 3 rd Divided Diff 4 th Divided Diff -0. 4837057 -0. 5489460 -0. 5786120 -0. 5715210 -0. 1087339 -0. 0494433 0. 0118183 0. 0658784 0. 0680685 0. 0018251

Newton Divided Difference: Example คาประมาณท x=1. 8 มคาเทาไร

Newton Divided Difference: Example คาประมาณท x=1. 8 มคาเทาไร

Forward Divided Difference

Forward Divided Difference

Forward Divided Difference

Forward Divided Difference

Forward Divided Difference

Forward Divided Difference

Backward Divided Difference

Backward Divided Difference

Backward Divided Difference

Backward Divided Difference

Backward Divided Difference

Backward Divided Difference

Newton Divided Difference: Example

Newton Divided Difference: Example

xi 1. 0 f(xi)=f[xi] 0. 7651977 1. 3 0. 6200860 1. 6 0. 4554022

xi 1. 0 f(xi)=f[xi] 0. 7651977 1. 3 0. 6200860 1. 6 0. 4554022 1. 9 0. 2818186 1 st Divided Diff 2 nd Divided Diff 3 rd Divided Diff 4 th Divided Diff -0. 4837057 -0. 5489460 -0. 5786120 -0. 1087339 -0. 0494433 0. 0118183 0. 0658784 0. 0680685 Example (Newton -0. 5715210 Divided Difference) 2. 2 0. 1103623 0. 0018251

Newton Divided Difference: Example

Newton Divided Difference: Example

Newton Divided Difference: Example xi 1. 0 f(xi)=f[xi] 0. 7651977 1. 3 0. 6200860

Newton Divided Difference: Example xi 1. 0 f(xi)=f[xi] 0. 7651977 1. 3 0. 6200860 1. 6 0. 4554022 1. 9 0. 2818186 2. 2 0. 1103623 1 st Divided Diff 2 nd Divided Diff 3 rd Divided Diff 4 th Divided Diff -0. 4837057 -0. 5489460 -0. 5786120 -0. 5715210 -0. 1087339 -0. 0494433 0. 0118183 0. 0658784 0. 0680685 0. 0018251

Newton Divided Difference: Example

Newton Divided Difference: Example

Hermite Interpolation

Hermite Interpolation

Hermite Interpolation

Hermite Interpolation

Hermite Interpolation

Hermite Interpolation

Hermite Interpolation

Hermite Interpolation

Hermite Interpolation

Hermite Interpolation

Hermite Interpolation: Example

Hermite Interpolation: Example

Hermite Interpolation: Example

Hermite Interpolation: Example

Hermite Interpolation: Example

Hermite Interpolation: Example

Cubic Spline Interpolation

Cubic Spline Interpolation

Cubic Spline Interpolation

Cubic Spline Interpolation

Cubic Spline Interpolation

Cubic Spline Interpolation

Cubic Spline Interpolation

Cubic Spline Interpolation

Cubic Spline Interpolation

Cubic Spline Interpolation

Cubic Spline Interpolation

Cubic Spline Interpolation

Cubic Spline Interpolation

Cubic Spline Interpolation

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Cubic Spline: Example

Least Square Method

Least Square Method

Least Square Method

Least Square Method

Least Square Method

Least Square Method

Least Square Method

Least Square Method

Least Square Method: Example

Least Square Method: Example

Least Square Method: Example

Least Square Method: Example

Least Square Method: Example

Least Square Method: Example

Least Square Method

Least Square Method

Least Square Method: Example

Least Square Method: Example

Least Square Method: Example

Least Square Method: Example

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Bilinear interpolation Cubic interpolation 604415102 5bilinear interpolation 5cubicBilinear interpolation Cubic interpolation 604415102 5bilinear interpolation 5cubic
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Numerical Analysis TOPIC Interpolation DEFINITION Interpolation is theNumerical Analysis TOPIC Interpolation DEFINITION Interpolation is the
Interpolation and Approximation 1 Lagrange Interpolation n TheInterpolation and Approximation 1 Lagrange Interpolation n The
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Interpolation and Polynomial Approximation Problem Let x 0Interpolation and Polynomial Approximation Problem Let x 0
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Approximation schemes Scheduling problems Polynomial Time Approximation SchemeApproximation schemes Scheduling problems Polynomial Time Approximation Scheme
Polynomial Division Dividing one polynomial by another polynomialPolynomial Division Dividing one polynomial by another polynomial
YMBOIKO polynomial Expression Variable polynomial X X polynomialYMBOIKO polynomial Expression Variable polynomial X X polynomial
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YMBOIKO polynomial Expression Variable polynomial X X polynomialYMBOIKO polynomial Expression Variable polynomial X X polynomial
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