The Pascal matrix is known in the history of Mathematics much before the name of the great scientist Blaise Pascal. The beauty of such matrix structure and its use in different branch of mathematics connected with the names Bernoulli, Bernstein, Vandermonde, Frobenius, Stirling, and others has been recognized and studied in the quoted literature. Our goal here is to consider the Pascal matrix sequence made by Pascal matrices of increasing matrix-size and few variations and to present an asymptotic study of the singular values and of the conditioning, using recent techniques from asymptotic linear algebra. The results are quite surprising and equally beautiful: they are critically discussed together with few representative numerical experiments.
The Pascal matrix sequence: an asymptotic study of the conditioning and of its Weyl singular value distribution
Lidia Aceto
;
2026-01-01
Abstract
The Pascal matrix is known in the history of Mathematics much before the name of the great scientist Blaise Pascal. The beauty of such matrix structure and its use in different branch of mathematics connected with the names Bernoulli, Bernstein, Vandermonde, Frobenius, Stirling, and others has been recognized and studied in the quoted literature. Our goal here is to consider the Pascal matrix sequence made by Pascal matrices of increasing matrix-size and few variations and to present an asymptotic study of the singular values and of the conditioning, using recent techniques from asymptotic linear algebra. The results are quite surprising and equally beautiful: they are critically discussed together with few representative numerical experiments.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
