In this post, we attempt to unravel the mysteries of the “magic” constant found in the fast inverse sqrt method in an intuitive fashion.

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## Algorithm

# Calculating Modified Fibonacci Numbers, Quickly and Exactly

This is inspired by an article of similar name called Calculating Fibonacci Numbers, Quickly and Exactly. Consider the a modified fibonacci sequence given by the recurrence . We shall look at various algebraic and analytic properties of this sequence, find two algorithms that computes in time, and finally look at a motivating example where we need to compute this sequence quickly and exactly.

# Infinity Norm of the Inverse of Lower Bidiagonal Matrices

We consider the problem of efficiently computing the infinity norm of the inverse of a lower bidiagonal matrix L in linear time.

# Interval Scheduling Problem

Let’s consider the *Interval Scheduling Problem*, in which we have a set of n requests ; the request corresponds to an interval of time starting at and finishing at , or request spans interval . Suppose that a subset of the requests is *compatible* if no two of them overlap in time; find the largest compatible subset of any set of requests in a reasonable number of steps.