CSC_349_HANDOUT#27

# CSC_349_HANDOUT#27 - COMPUTER SCIENCE 349A Handout Number...

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1 COMPUTER SCIENCE 349A Handout Number 27 DEGREE OF PRECISION OF A QUADRATURE FORMULA The degree of precision of a quadrature formula is a measure of its accuracy or power. It is an integer number that indicates the degree (or order) of the set of all polynomials that the quadrature formula will integrate exactly. The larger the degree of precision, the more accurate or powerful is the quadrature formula because it will integrate exactly a larger set of polynomials, and this is a very good indicator that it will therefore integrate non-polynomial functions more accurately. Definition If a quadrature formula = n i i i x f a 0 ) ( computes the exact value of b a dx x f ) ( whenever ) ( x f is a polynomial of degree d , but = n i i i x f a 0 ) ( b a dx x f ) ( for some polynomial ) ( x f of degree d + 1, then the degree of precision of the quadrature formula is d . Note . If ) ( x f is a polynomial of degree d , then = = d i i i x c x f 0 ) ( and = = d i b a i i b a dx x c dx x f 0 ) (.

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CSC_349_HANDOUT#27 - COMPUTER SCIENCE 349A Handout Number...

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