09-Newtons-Method-4UP

09-Newtons-Method-4UP - Newtons method Examples...

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Unformatted text preview: Newtons method Examples Implementation details Newtons Method Dhavide Aruliah UOIT MATH 2070U c D. Aruliah (UOIT) Newtons Method MATH 2070U 1 / 15 Newtons method Examples Implementation details Newtons Method 1 Newtons method 2 Examples 3 Implementation details c D. Aruliah (UOIT) Newtons Method MATH 2070U 2 / 15 Newtons method Examples Implementation details Basic geometric idea x ( k + 1 ) found by extending tangent line from ( x ( k ) , f ( x ( k ) )) Next iterate x ( k + 1 ) is the x-intercept of tangent line Given iterate x ( k ) that approximates zero of f , approximate the graph of f by the tangent line L Follow L to P (where it cuts x-axis) x ( k + 1 ) defined as x-coordinate of point P c D. Aruliah (UOIT) Newtons Method MATH 2070U 4 / 15 Newtons method Examples Implementation details Basic geometric idea Value x ( k + 1 ) is hoped to be closer to true zero x * of f ( x * ) = 0 than the original iterate x ( k ) Looking at graph, we have (from point-slope formula) f ( x ( k ) ) = f ( x ( k ) )- x ( k )- x ( k + 1 ) ....
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09-Newtons-Method-4UP - Newtons method Examples...

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