Papers by M. Warmus

Precursory papers on interval analysis
by M. Warmus

Here we present good quality scans of the two early papers of Mieczyslaw Warmus (with permission of the Editors, Bulletin of the Polish Academy of Sciences). Thanks are also due to Marcin Adamski from Publications Department of the Mathematical Institute of the PAS for providing good quality originals for scanning.

For the biography of Warmus see recent books presented at the Warmus site: [Polish edition, English edition]

The first paper (1956)

This paper contains, among others, the first published formulae for interval arithmetic operations in both endpont and midpoint-radius formulations, and the definition of the centered outer multiplication (see my paper with Svetoslav Markov in BIT).

M. Warmus,
Calculus of Approximations.
Bull. Acad. Polon. Sci., Cl. III,
vol. IV, No. 5 (1956), 253-259.

Click on the thumbnail of the required page to see the full-size 790x1250 image of the page appropriate for comfortable on-screen reading.
The 300 dpi (1580x2500) version is recommended for quality printing of the pages.
Page 253
p. 253
[300 dpi: 81KB]		 Page 254
p. 254
[300 dpi: 77KB]		 Page 255
p. 255
[300 dpi: 106KB]		 Page 256
p. 256
[300 dpi: 87KB]		 Page 257
p. 257
[300 dpi: 113KB]		 Page 258
p. 258
[300 dpi: 85KB]		 Page 259
p. 259
[300 dpi: 32KB]

The second paper (1961)

This paper contains, among others, the first appearance of an interval space diagram using midpoint-radius coordinates.

M. Warmus,
Approximations and Inequalities in the Calculus of Approximations.
Classification of Approximate Numbers.
Bull. Acad. Polon. Sci., Ser. math., astr. et phys.,
vol. IX, No. 4, (1961), 241-245.

Click on the thumbnail of the required page to see the full-size 790x1250 image of the page appropriate for comfortable on-screen reading.
The 300 dpi (1580x2500) version is recommended for quality printing of the pages.
Page 241
p. 241
[300 dpi: 60KB]		 Page 242
p. 242
[300 dpi: 92KB]		 Page 243
p. 243
[300 dpi: 96KB]		 Page 244
p. 244
[300 dpi: 115KB]		 Page 245
p. 245
[300 dpi: 95KB]

Back to:

[Button:] Interval analysis and computation

See also:

[Button:] Qualitative Analysis Group
[Button:] Our publications on intervals
[Button:] Diagrammatics

[IPPT PAN] our Institute [CSlogo] my Department
Maintained by Zenon Kulpa
Last updated Jan 9, 2008