linear-algebra   865

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[1709.09022] On Integer Images of Max-plus Linear Mappings
Let us extend the pair of operations (max,+) over real numbers to matrices in the same way as in conventional linear algebra. We study integer images of max-plus linear mappings. The question whether Ax (in the max-plus algebra) is an integer vector for at least one x has been studied for some time but polynomial solution methods seem to exist only in special cases. In the terminology of combinatorial matrix theory this question reads: is it possible to add constants to the columns of a given matrix so that all row maxima are integer? This problem has been motivated by attempts to solve a class of job-scheduling problems. We present two polynomially solvable special cases aiming to move closer to a polynomial solution method in the general case.
representation  linear-algebra  out-of-the-box  mathematics  algebra  nudge-targets  consider:looking-to-see  consider:representation 
16 days ago by Vaguery
Gonum
Gonum is a set of packages designed to make writing numeric and scientific algorithms productive, performant, and scalable.

Gonum contains libraries for matrices and linear algebra; statistics, probability distributions, and sampling; tools for function differentiation, integration, and optimization; network creation and analysis; and more.

We encourage you to get started with Go and Gonum if:

- You are tired of sluggish performance, and fighting C and vectorization.
You are struggling with managing programs as they grow larger.
- You struggle to re-use – even the code you tried to make reusable.
- You would like easy access to parallel computing.
- You want code to be fully transparent, and want the ability to read the source code you use.
- You’d like a compiler to catch mistakes early, but hate fighting linker and unintelligible compile errors.
golang  numeric  library  math  numeric-computing  linear-algebra  machinelearning 
16 days ago by newtonapple
ekmett/sparse: sparse matrices in Morton order
A sparse linear algebra playground based on Morton ordering
linear-algebra 
24 days ago by FTS
FLAME project
The objective of the FLAME project is to transform the development of dense linear algebra libraries from an art reserved for experts to a science that can be understood by novice and expert alike. Rather than being only a library, the project encompasses a new notation for expressing algorithms, a methodology for systematic derivation of algorithms, Application Program Interfaces (APIs) for representing the algorithms in code, and tools for mechanical derivation, implementation and analysis of algorithms and implementations.
linear-algebra  library  software  to-understand 
28 days ago by Vaguery
MIT 18.06SC Linear Algebra Recitations, Fall 2011 - YouTube (playlist)
<< MIT 18.06SC Linear Algebra Recitations, Fall 2011
37 videos

MIT OpenCourseWare
Instructor: Gilbert Strang

The Help Session Videos were developed by: Martina Balagovic, Linan Chen, Benjamin Harris, Ana Rita Pires, David Shirokoff, Nikola Kamburov
>>
mit-18.06  online-courses  videos  linear-algebra 
4 weeks ago by absfac
MIT 18.06 Linear Algebra, Spring 2005 - YouTube (playlist)
<<
MIT 18.06 Linear Algebra, Spring 2005
35 videos

MIT OpenCourseWare
Instructor: Prof. Gilbert Strang

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. *Please note that lecture 4 is unavailable in a higher quality format.
>>
videos  online-courses  linear-algebra  mit  mit-18.06 
4 weeks ago by absfac
Clojure Numerics, Part 2 - General Linear Systems and LU Factorization
Solving systems of linear equations is a staple food of linear algebra. It can be applied as a part of many machine learning tasks, although it is not always obvious to spot the opportunity. Here, we explore how triangular systems are the foundation that we need to internalize well. We concentrate on computational details, and transformations of general systems to triangular systems . Neanderthal offers many functions to help us in this quest.
Clojure  linear-algebra  library  nudge  Klapaucius-library  to-do 
4 weeks ago by Vaguery

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