[PDF] 43 = (((((1 · 2) + 0) · 2 + 1) · 2 + 0) · 2 + 1)





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2.6 Zeros of Polynomials and Horners Method

using Horner's method in (n-1) multiplications and (n-1) additions. 2. Horner's method is nested arithmetic. 5. Page 6. • Example.



A Note on Horners Method

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43 = (((((1 · 2) + 0) · 2 + 1) · 2 + 0) · 2 + 1)

Horner's rule is an efficient algorithm for converting a number Horner's rule is also useful for evaluating a polynomial and Taylor coefficients.



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13-May-2007 The algorithm can be written as follows: # Horner's method to evaluate a polynomial at a point. # Inputs are the polynomial coefficients P0 ...n.



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As a division algorithm Horner's method is a nesting technique requiring only n multiplications and n additions to evaluate an arbitrary nth-degree polynomial 



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PDF Here we present an application of Horner's method in evaluating the sequence of Stirling numbers of the second kind Based on the method we also



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8 jan 2011 · Horner's Algorithm - may be used to convert one base to another Notice it required 6 divisions to find the binary form of 53 53 = 2?26 + 1



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Horner's rule is an efficient algorithm for converting a number Horner's rule is also useful for evaluating a polynomial and Taylor coefficients



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25 nov 2004 · 1 1 Horner's method as Horner's method This is also the procedure behind synthetic division Use Horner to evaluate the polynomial

  • What is Horner's method used for?

    Horner's rule for polynomial division is an algorithm used to simplify the process of evaluating a polynomial f(x) at a certain value x = x0 by dividing the polynomial into monomials (polynomials of the 1st degree).

  • What is the Horner's method of stability?

    Horner's method for computing a polynomial both reduces the number of multiplications and results in greater numerical stability by potentially avoiding the subtraction of large numbers. It is based on successive factorization to eliminate powers of greater than 1.
  • The first studies of fear of success (Horner, 1968) showed that the expectation (not necessarily in awareness) of negative consequences as a result of the pursuit or attainment of success aroused anxiety in female subjects. Similar expectations were significantly less evident in male subjects.
43 = (((((1 · 2) 0) · 2 1) · 2 0) · 2 1)

Horner"s Rule

Horner"srule is an efficient algorithm for converting a number written in basebinto its decimal notation. Horner"s rule is also useful for evaluating a polynomial, and Taylor coefficients. Evaluating polynomials by Horner"s rule is covered elsewhere in this course.

Horner"s Rule

Consider the natural number43. Writing43as a sum of powers of2implies its binary representation.

43=32+8+2+1

43=125+024+123+022+121+120

43=(10 1011)2

Horner"s rule writes converts

(10 1011)2to43from the most sig- nificant bit to the least significant bit.

43= (((((12) +0)2+1)2+0)2+1)

This multiplicity of parentheses is somewhat confusing, so let"s re- formulate it.

Horner"s Rule to Convert Binary to Decimal

To convert

(10 1011)2to decimal: 1. write the bit pattern to be converted (leave sufficient space between bits)

1 0 1 0 1 12.Next, bring down the leading 1

1 0 1 0 1 11

(Continued next slide) 1

Example Continued

Continuing from the previous slide.

3.

Multiply the 1by2and place it under the next bit.

1 0 1 0 1 1

21
4.

Add the values in the second column.

1 0 1 0 1 1

21 2
5.

Repeat the process.

Example Continued

Continuing from the previous slides.

Multiply2by2and add1.

1 0 1 0 1 1

2 41 2 5

Multiply5by2and add0.

1 0 1 0 1 1

2 4 101 2 5 10

2

Example Continued

Continuing from the previous slides.

Multiply10by2and add to1.

1 0 1 0 1 1

2 4 10 201 2 5 10 21

Multiply21by2and add1.

1 0 1 0 1 1

2 4 10 20 421 2 5 10 2143Therefore,

(10 1011)2=43.

Other Examples of Binary to Decimal Conversion

Here"s an example computation of Horner"s rule to convert bi- nary (1101 0100)2to decimal212.Horner"s Rule

1 1 0 1 0 1 0 0

2 6 12 26 52 106 2121 3 6 13 26 53 106212And here is a second example.

Horner"s Rule

1 0 0 0 1 1 1 1

2 4 8 16 34 70 1421 2 4 8 17 35 71143Therefore,

(1000 1111)2=143. 3

Converting Ternary to Decimal

You can also use Horner"s rule convert from bases other than2 to decimal. Here"s an example computation of Horner"s rule to convert ternary (210)3to decimal21.Horner"s Rule base=32 1 0

6 212 721Converting Hexadecimal to Decimal

Here"s an example computation of Horner"s rule to convert hex- adecimal (CAFE)16to decimal51966.Horner"s Rule base=16C A F E

192 3232 5195212 202 324751966Because

(DEAD CODE)16is an interesting string you might want to convert it to decimal. 4quotesdbs_dbs28.pdfusesText_34
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