FLOP

A FLOP is a “floating-point operations”. One addition, subtraction, multiplication, or division of two floating-point numbers.

Basic Linear Algebra Subroutines

BLAS Level 1

Vector-Vector operations

• inner product \(x^{T}y\) which is \(2n-1\) flops
• sum \(x+y\) and scale \(\alpha x\) which is \(n\) flops

BLAS Level 2

Matrix-vector product

\(y = Ax\) with \(A \in \mathbb{R}^{m \times n}\)

• standard multiply \(m\qty(2n - 1)\)
• \(2N\) if \(A\) is sparse with \(N\) non-zero elements
• \(2p\qty(n+m)\) if \(A\) is given as \(A = UV^{T}\), where \(U \in \mathbb{R}^{m \times p}\) and \(V \in \mathbb{R}^{n \times p}\), which is called a “banded” matrix (sparse everywhere except for a strip nexht to diagonal)

BLAS Level 3

Matrix-matrix operations

Key Sequence

Notation

New Concepts

• Numerical Linear Algebra

Important Results / Claims

Questions

Interesting Factoids

Key Sequence

Notation

New Concepts

• iterative method
  • descent method
• convergence of self-concordant functions

Important Results / Claims

Questions

Interesting Factoids

Implications: rapid population aging. 1-child policy means that cost of pensions, health care, and social services will thus rise.

• 1 in 6 now above 60
• 1 in 4 above 2030
• 1 in 3 by 2050

“get old before getting rich”

demography

1980-2010

• low dependency ratios
• high household savings rate
• large lavor supply
• “age of abundance”

decline

• rapidly aging population
• rapidly rising dependency ratios
• ageing population / rising health / retirement costs
• shrikning labor force, rising wages
• declining of deposits in bank system
• less capital

resulting dynamics

• labor force shrinking by 2 million workers per year
• manufacturing wages rising faster
• labor cost advantage almost gone

wages keep going up

You got the lights on in the afternoon

And the nights are drawn out long

And you’re kissin’ to cut through the gloom

With a cough drop coloured tongue

And you were sittin’ in the corner with the coats all piled high

And I thought you might be mine

In a small world, on an exceptionally rainy Tuesday night

In the right place and time

When the zeros line up on the 24 hour clock