- Docente: Valeria Simoncini
- Credits: 8
- SSD: MAT/08
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 6061)
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from Sep 23, 2025 to Dec 19, 2025
Learning outcomes
At the end of the course, students know the first part of fundamental problems in Scientific Computing related to the numerical solution of linear algebra problems and nonlinear equations. They know and can use the principal methods to solve these problems efficiently on a computer. Students can use the acquired knowledge to study and develop algorithms for solving problems arising in applications, and they can critically analyze the obtained results. Students can work independently or in a group.
Course contents
Floating point arithmetic.
Numerical linear algebra: Aspects of matrix analysis. direct methods for the solution of a linear system; iterative methods for the solution of a linear system; Householder reflections and Givens rotations; orthogonal factorizations: QR and linear least squares solution. Numerical methods for eigenvalues and eigenvectors approximation.
Nonlinear equations: bisection, newton method and its variants, fixed point methods. Implementation and convergence analysis.
Readings/Bibliography
- "Matematica Numerica", A. Quarteroni, R. Sacco, F. Saleri, III ed., Springer 2008 e succ.
- "Analisi Numerica - metodi modelli applicazioni", V. Comincioli, McGraw-Hill 1995.
- "Introduction to Numerical Analysis", J. Stoer, R. Bulirsch, II ed., Springer 1993 e succ.
- "Applied Numerical Linear Algebra", J. W. Demmel, SIAM 1997.
- "Metodi numerici per l'algebra lineare", D. Bini, M. Capovani, O. Menchi, Zanichelli 1988.
additional texts
- "Accuracy and Stability of Numerical Algorithms", N. J. Higham, SIAM 1996.
- "Matrix computations", G. H. Golub e C. F. Van Loan, The Johns Hopkins University Press, 1996 e succ.
and others
Lecture notes
website: www.dm.unibo.it/~simoncin/
Teaching methods
Use of blackboard in class, computer tablet writing and other computer software.
Extra material provided in the course website and on Virtuale.
Assessment methods
Lab Test (propedeutical for the oral part of the exam),
Written test on the topics presented during the semester,
The written test is followed by an oral test, on the same topics.
Teaching tools
ex cathedra teaching plus computer lab sessions.
Office hours
See the website of Valeria Simoncini