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Numerical Linear Algebra with Applications by William Ford

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Chapter 9

Algorithms

Abstract

This chapter defines an algorithm and develops pseudocode for expressing an algorithm. As examples, pseudocode is presented for the inner product, the Frobenius matrix norm, and matrix multiplication. Block matrices are briefly discussed using 2 × 2 block matrices. Algorithm efficiency is defined in terms of flop count, and Big-O notation is intuitively developed for expressing flop count. It is made clear that a larger flop count does not guarantee a faster algorithm. Higher memory requirements, poor coding, the ability parallelize one algorithm and not another are factors that must be considered. Truncation error occurs when only a finite number of terms of an infinite series are used; for instance, one could ...

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