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To measure the work completed by an algorithm, we often count flops, the number of floating-point additions subtractions, multiplications, or divisions. Let a be a real number, m, n, and r be positive integers, u, v, and x be n-dimensional column vectors, y be an m-dimensional column vector, A be an m x r matrix, B be an r x n matrix, and C' be an m x n matrix. Give the number of flops required for each of the following calculations. a. The dot product of vectors u and v b. y + Cx c. C+YxT d. C + AB

To measure the work completed by an algorithm, we often count flops, the number of floating-point additions subtractions, multiplications, or divisions. Let a be a real number, m, n, and r be positive integers, u, v, and x be n-dimensional column vectors, y be an m-dimensional column vector, A be an m x r matrix, B be an r x n matrix, and C' be an m x n matrix. Give the number of flops required for each of the following calculations. a. The dot product of vectors u and v b. y + Cx c. C+YxT d. C + AB

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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To measure the work completed by an algorithm, we often count flops, the number of floating-point additions subtractions, multiplications, or divisions. Let \( a \) be a real number, \( m, n, \) and \( r \) be positive integers, \( \mathbf{u}, \mathbf{v}, \) and \( \mathbf{x} \) be \( n \)-dimensional column vectors, \( \mathbf{y} \) be an \( m \)-dimensional column vector, \( A \) be an \( m \times r \) matrix, \( B \) be an \( r \times n \) matrix, and \( C \) be an \( m \times n \) matrix. Give the number of flops required for each of the following calculations. a. The dot product of vectors \( \mathbf{u} \) and \( \mathbf{v} \) b. \( \mathbf{y} + C \mathbf{x} \) c. \( C + \mathbf{y} \mathbf{x}^T \) d. \( C + AB \)
Transcribed Image Text:To measure the work completed by an algorithm, we often count flops, the number of floating-point additions subtractions, multiplications, or divisions. Let \( a \) be a real number, \( m, n, \) and \( r \) be positive integers, \( \mathbf{u}, \mathbf{v}, \) and \( \mathbf{x} \) be \( n \)-dimensional column vectors, \( \mathbf{y} \) be an \( m \)-dimensional column vector, \( A \) be an \( m \times r \) matrix, \( B \) be an \( r \times n \) matrix, and \( C \) be an \( m \times n \) matrix. Give the number of flops required for each of the following calculations. a. The dot product of vectors \( \mathbf{u} \) and \( \mathbf{v} \) b. \( \mathbf{y} + C \mathbf{x} \) c. \( C + \mathbf{y} \mathbf{x}^T \) d. \( C + AB \)
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