The following problem is based on a problem in section 4 of the book “Model Building in Mathematical Programming”. I’ve modified some aspects of it but it’s similar in nature. In my previous post I went over a basic method for solving linear programming problems with the example of a water plant that made two products.

Problem Description

In this post I will talk about using the same idea for linear programming problems with multiple subproblems. In this case we’ll be looking at a company which has two factories, factory A and factory B. The company makes bearings and produces two products…

I haven’t written anything on here since June 2020. I had originally planned to write some more about linear algebra and I’m not sure what happened. In college I briefly did some research on using linear programming to help reduce noise in signals. At that point I don’t think I had much of an understanding of optimization. Over the past few months I spent some time learning about linear programming. This article will just be about interpreting simplistic problems and using basic tools to solve them.

Background

I’ll note that I know there have been several other posts about this topic…

Contents

• Intro
• More on the SVD
• Conditioning
• References

Intro

The following is a continuation of the previous story ‘A Short Introduction to Numerical Linear Algebra — Part 1’. If you haven’t read it yet, then you may find it useful to read before. You can find it below.

This post will continue some of the introduction to the Singular Value Decomposition and conditioning.

More on the SVD

If you’ve followed along to this point then you’ve probably seen you can rewrite a matrix as a product of several other matrices. There are tons of other matrix decompositions that are different than the SVD and each has…

Table Of Contents

• Introduction
• Norms
• SVD

Introduction

I was originally planning on writing a piece or a few short pieces on non-standard matrix decompositions and or new methods in matrix decompositions. Instead, I’ve decided to write an overview of numerical linear algebra so I can simply refer back to it. This is partly because most of the advances I’ve seen in matrix factorizations actually borrow previous ideas or factorizations and use them in different ways.

In order to follow along, I’ll assume that you have some degree of mathematical background and preferably have taken linear algebra though it might not be necessary. Understanding mathematical…

I’ve decided to make this type of story more frequent. I’m currently considering doing it every week. The subject of this story is about the math in the movie, ‘The Accountant’. There are several movies named, ‘The Accountant’, so to clarify I mean the 2016 action-thriller with Ben Affleck. The movie itself has very little to do with mathematics however a central part of the plot has to do with an interesting realization about numbers and how real-life purchase data is distributed.

Movie Synopsis

The movie starts off showing parents talking to a specialist about their autistic child and what expectations they’d…

The following was originally going to be about non-standard matrix decompositions, however it is going to take some more time than I expected to format it. Instead I was inspired to write about a piece of math I saw on a TV show. I am using the current title because I anticipate that I may find other interesting problems on TV or in the movies.

I’ve been binging the TV series, ‘The Good Doctor’. It’s a medical drama based on a Korean TV series with the same name. The show focuses on a surgical resident called Shaun Murphy who is…

The following is an ongoing exercise to look at how to pre-aggregate data to quickly summarize it. I was previously using a database I generated that looks like this.

The goal of this originally was to find a quick way of summarizing sales data for the purchases and the associated stores. I had previously posted a query like this and said there are some issues with using the ‘purchase_start’ as an index.

select 
 inv.store_id,
 SUM(CASE WHEN product_type = 'Burger' THEN cost Else 0 End) 'Total Burger Revenue',
    SUM(CASE WHEN product_type = 'Fish' THEN cost Else 0…

This is the second part of a series looking at how to generate some random data and perform some basic SQL queries on that data. I had previously posted some code however I have cleaned that code up and put in its own repository for people to play with now.

You can find the repository here if you want to use it. I made a few improvements that are worth talking about.

Improvements

The issues with the last iteration were the length of time it took to generate the data and the insert the data. In order to decrease the time…