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- Siegfried M. Rump

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
32
Citations
5,847
202
World Ranking
2347
National Ranking
142

- Algebra
- Complex number
- Mathematical analysis

Siegfried M. Rump mostly deals with Algorithm, Rounding, Floating point, Round-off error and Condition number. His Algorithm research incorporates themes from Complex number, Multiplication, Numerical analysis and Interval. His Rounding study incorporates themes from Cholesky decomposition, Hermitian matrix and Combinatorics.

The various areas that he examines in his Floating point study include Arbitrary-precision arithmetic and Arithmetic. His Arbitrary-precision arithmetic research integrates issues from Arithmetic function, Sparse matrix and MATLAB. His Condition number research is multidisciplinary, relying on both Circulant matrix, Linear system and Toeplitz matrix, Pure mathematics.

- INTLAB — INTerval LABoratory (873 citations)
- Accurate Sum and Dot Product (307 citations)
- Verification methods: Rigorous results using floating-point arithmetic (185 citations)

His primary areas of investigation include Algorithm, Floating point, Rounding, Linear system and Matrix. His work deals with themes such as Interval arithmetic, Interval, Numerical analysis and Dot product, which intersect with Algorithm. His study looks at the relationship between Floating point and fields such as Arithmetic, as well as how they intersect with chemical problems.

His Rounding study combines topics in areas such as Arithmetic underflow, Round-off error, Machine epsilon, Simple and IEEE floating point. His Linear system study combines topics from a wide range of disciplines, such as Correctness, H matrix, Mathematical optimization, Toeplitz matrix and Applied mathematics. His Matrix research includes elements of Discrete mathematics, Bounded function and Combinatorics.

- Algorithm (32.48%)
- Floating point (23.93%)
- Rounding (28.21%)

- Combinatorics (21.37%)
- Matrix (22.22%)
- Real number (5.98%)

His scientific interests lie mostly in Combinatorics, Matrix, Real number, Applied mathematics and Floating point. His work on Disjoint sets as part of his general Combinatorics study is frequently connected to Perturbation, thereby bridging the divide between different branches of science. His Matrix research is multidisciplinary, incorporating elements of Piecewise linear function, Eigenvalues and eigenvectors, Product and Absolute value equation.

His studies in Real number integrate themes in fields like Well-defined, Recursion, Arithmetic, Rounding and Extended precision. His work carried out in the field of Rounding brings together such families of science as Fixed point and Limit. His work in Floating point tackles topics such as Round-off error which are related to areas like Discrete mathematics, Square root and Base.

- On relative errors of floating-point operations: Optimal bounds and applications (17 citations)
- Sharp estimates for perturbation errors in summations (6 citations)
- Bounds for the determinant by Gershgorin circles (3 citations)

- Algebra
- Complex number
- Real number

Siegfried M. Rump mainly investigates Combinatorics, Floating point, Real number, Round-off error and Matrix. His studies examine the connections between Combinatorics and genetics, as well as such issues in Diagonal, with regards to Identity matrix, Upper and lower bounds, Matrix norm and Toeplitz matrix. His Real number study frequently links to other fields, such as Rounding.

The study incorporates disciplines such as Standard algorithms, Matrix multiplication, Cholesky decomposition and Arithmetic in addition to Rounding. His work is dedicated to discovering how Round-off error, Square root are connected with Unit, Arithmetic underflow, Function, Base and Expression and other disciplines. His Matrix research incorporates elements of Disjoint sets, Eigenvalues and eigenvectors and Product.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

INTLAB — INTerval LABoratory

Siegfried M. Rump.

Developments in Reliable Computing **(1999)**

1472 Citations

INTLAB — INTerval LABoratory

Siegfried M. Rump.

Developments in Reliable Computing **(1999)**

1399 Citations

Accurate Sum and Dot Product

Takeshi Ogita;Siegfried M. Rump;Shin'ichi Oishi.

SIAM Journal on Scientific Computing **(2005)**

499 Citations

Verification methods: Rigorous results using floating-point arithmetic

Siegfried M. Rump.

Acta Numerica **(2010)**

316 Citations

Verification methods: Rigorous results using floating-point arithmetic

Siegfried M. Rump.

Acta Numerica **(2010)**

277 Citations

Verification methods for dense and sparse systems of equations

Siegfried M. Rump.

**(1994)**

272 Citations

Solving algebraic problems with high accuracy

Siegfried M. Rump.

Proc. of the symposium on A new approach to scientific computation **(1983)**

260 Citations

Accurate Floating-Point Summation Part I: Faithful Rounding

Siegfried M. Rump;Takeshi Ogita;Shin'ichi Oishi.

SIAM Journal on Scientific Computing **(2008)**

204 Citations

Fast and Parallel Interval Arithmetic

Siegfried M. Rump.

Bit Numerical Mathematics **(1999)**

194 Citations

Kleine Fehlerschranken bei Matrixproblemen

Siegfried M. Rump.

**(1980)**

129 Citations

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