# Method for data compression by associating complex numbers with files of data values

## Abstract

A method for compressing data for storage or transmission is disclosed. Given a complex polynomial and a value assigned to each root, a root generated data file (RGDF) is created, one entry at a time. Each entry is mapped to a point in a complex plane. An iterative root finding technique is used to map the coordinates of the point to the coordinates of one of the roots of the polynomial. The value associated with that root is assigned to the entry. An equational data compression (EDC) method reverses this procedure. Given a target data file, the EDC method uses a search algorithm to calculate a set of m complex numbers and a value map that will generate the target data file. The error between a simple target data file and generated data file is typically less than 10%. Data files can be transmitted or stored without loss by transmitting the m complex numbers, their associated values, and an error file whose size is at most one-tenth of the size of the input data file. 4 figs.

- Inventors:

- Issue Date:

- Research Org.:
- Univ. of California (United States)

- Sponsoring Org.:
- USDOE, Washington, DC (United States)

- OSTI Identifier:
- 570421

- Patent Number(s):
- 5717787

- Application Number:
- PAN: 8-633,386

- Assignee:
- Univ. of California, Oakland, CA (United States)

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Patent

- Resource Relation:
- Other Information: PBD: 10 Feb 1998

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; DATA PROCESSING; DATA TRANSMISSION; MEMORY DEVICES; ALGORITHMS; POLYNOMIALS

### Citation Formats

```
Feo, J T, Hanks, D C, and Kraay, T A.
```*Method for data compression by associating complex numbers with files of data values*. United States: N. p., 1998.
Web.

```
Feo, J T, Hanks, D C, & Kraay, T A.
```*Method for data compression by associating complex numbers with files of data values*. United States.

```
Feo, J T, Hanks, D C, and Kraay, T A. Tue .
"Method for data compression by associating complex numbers with files of data values". United States.
```

```
@article{osti_570421,
```

title = {Method for data compression by associating complex numbers with files of data values},

author = {Feo, J T and Hanks, D C and Kraay, T A},

abstractNote = {A method for compressing data for storage or transmission is disclosed. Given a complex polynomial and a value assigned to each root, a root generated data file (RGDF) is created, one entry at a time. Each entry is mapped to a point in a complex plane. An iterative root finding technique is used to map the coordinates of the point to the coordinates of one of the roots of the polynomial. The value associated with that root is assigned to the entry. An equational data compression (EDC) method reverses this procedure. Given a target data file, the EDC method uses a search algorithm to calculate a set of m complex numbers and a value map that will generate the target data file. The error between a simple target data file and generated data file is typically less than 10%. Data files can be transmitted or stored without loss by transmitting the m complex numbers, their associated values, and an error file whose size is at most one-tenth of the size of the input data file. 4 figs.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1998},

month = {2}

}