Direct Methods for the Solution of Linear Systems

  • Alfio Quarteroni
  • Riccardo Sacco
  • Fausto Saleri
Part of the Texts in Applied Mathematics book series (TAM, volume 37)


A system of m linear equations in n unknowns consists of a set of algebraic relations of the form
where x j are the unknowns, aij are the coefficients of the system and bi are the components of the right hand side. System (3.1) can be more conveniently written in matrix form as
where we have denoted by A = (aij) ∈ ℂm×n the coefficient matrix, by b=(bi) ∈ (ℂm the right side vector and by x=(xi) ∈ ℂm the unknown vector, respectively. We call a solution of (3.2) any n-tuple of values xi which satisfies (3.1).


Linear System Diagonal Entry Triangular Matrix Cholesky Factorization Sparsity Pattern 
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Copyright information

© Springer Science+Business Media New York 2007

Authors and Affiliations

  • Alfio Quarteroni
    • 1
  • Riccardo Sacco
    • 2
  • Fausto Saleri
    • 3
  1. 1.Department of MathematicsEcole Polytechnique, Fédérale de LausanneLausanneSwitzerland
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  3. 3.Dipartimento di Matematica, “F. Enriques”Università degli Studi di MilanoMilanItaly

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