Accurate bidiagonal decompositions of Cauchy–Vandermonde matrices of any rank
Jorge Delgado
Departamento de Matemática Aplicada, Universidad de Zaragoza, Edificio Torres Quevedo, Zaragoza, Spain
Search for more papers by this authorCorresponding Author
Plamen Koev
Department of Mathematics, San Jose State University, San Jose, California, USA
Correspondence
Plamen Koev, Department of Mathematics, San Jose State University, San Jose, CA 95192, USA.
Email: [email protected]
Search for more papers by this authorAna Marco
Departamento de Física y Matemáticas, Universidad de Alcalá, Alcalá de Henares, Madrid, Spain
Search for more papers by this authorJosé-Javier Martínez
Departamento de Física y Matemáticas, Universidad de Alcalá, Alcalá de Henares, Madrid, Spain
Search for more papers by this authorJuan Manuel Peña
Departamento de Matemática Aplicada, Universidad de Zaragoza, Edificio de Matemáticas, 50019 Zaragoza, Spain
Search for more papers by this authorPer-Olof Persson
Department of Mathematics, University of California, Berkeley, California, USA
Search for more papers by this authorSteven Spasov
Columbia University, New York, 10027 New York, USA
Search for more papers by this authorJorge Delgado
Departamento de Matemática Aplicada, Universidad de Zaragoza, Edificio Torres Quevedo, Zaragoza, Spain
Search for more papers by this authorCorresponding Author
Plamen Koev
Department of Mathematics, San Jose State University, San Jose, California, USA
Correspondence
Plamen Koev, Department of Mathematics, San Jose State University, San Jose, CA 95192, USA.
Email: [email protected]
Search for more papers by this authorAna Marco
Departamento de Física y Matemáticas, Universidad de Alcalá, Alcalá de Henares, Madrid, Spain
Search for more papers by this authorJosé-Javier Martínez
Departamento de Física y Matemáticas, Universidad de Alcalá, Alcalá de Henares, Madrid, Spain
Search for more papers by this authorJuan Manuel Peña
Departamento de Matemática Aplicada, Universidad de Zaragoza, Edificio de Matemáticas, 50019 Zaragoza, Spain
Search for more papers by this authorPer-Olof Persson
Department of Mathematics, University of California, Berkeley, California, USA
Search for more papers by this authorSteven Spasov
Columbia University, New York, 10027 New York, USA
Search for more papers by this authorAbstract
We present a new decomposition of a Cauchy–Vandermonde matrix as a product of bidiagonal matrices which, unlike its existing bidiagonal decompositions, is now valid for a matrix of any rank. The new decompositions are insusceptible to the phenomenon known as subtractive cancellation in floating point arithmetic and are thus computable to high relative accuracy. In turn, other accurate matrix computations are also possible with these matrices, such as eigenvalue computation amongst others.
CONFLICT OF INTEREST STATEMENT
The authors have no conflicts of interest to disclose.
Open Research
DATA AVAILABILITY STATEMENT
Data sharing is not applicable to this article as no new data were created or analyzed in this study.
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