# Tag Info

Accepted

### Inequality caused by float inaccuracy

In typical floating point implementations, the result of a single operation is produced as if the operation was performed with infinite precision, and then rounded to the nearest floating-point number....

Accepted

Accepted

### Inequality caused by float inaccuracy

The binary floating point format supported by computers is essentially similar to decimal scientific notation used by humans. A floating-point number consists of a sign, mantissa (fixed width), and ...

### Fastest way to solve a system of linear equations

There is what you want to achieve, and there is reality, and sometimes they are in conflict. First you check if your problem is a special case that can be solved quicker, for example a sparse matrix. ...
Accepted

### numerically stable log1pexp calculation

Let $0 < \varepsilon \lll 1$ be the relative error bound of the floating-point system—$2^{-53}$ in IEEE 754 binary64 arithmetic. First, the naive formula ...

### Why are transcendental functions of large numbers inaccurate on computers?

Taking the sine of large numbers is a numerically unstable operation. Considering an argument like $10^{99}$, you can get a completely different value of the sine by adding, say $1$ to it. Think that ...
The partial convergents of the continued fraction of $x$ consists of all the best rational approximations of $x$; see Wikipedia, for example. A best rational approximation of $x$ is a rational number \$...