Numerical Analysis: Numerical Approximation
Course · 7.5 credits
Kursinnehåll: Approximationsproblemet: Normer, approximationsrum, Weierstrass sats. Bästa approximation i Euklidiska rum: Existens, entydighet, karakterisering av bästa approximanter, dualer. Konstruktion av bästa approximationer: Ortogonalitet, Tjebysjovpolynom, Haar-rum, utbytesalgoritmen.
The fundamental problem of approximation theory is to represent a possibly complicated function by simpler, easier to compute functions. In approximation theory it is usually assumed that the values of the function are known. This information is then used to construct an approximant. In numerical computation, information usually comes in a less explicit form. For example, the function may be the solution to a differential equation. Nevertheless, the two subjects of approximation and computation are closely related, and it is impossible to understand fully the possibilities in numerical computation without a good understanding of the elements of constructive approximation. This course will give an overview of basic classical approximation theory, i.e., best and good approximation from a finite family of functions in specific normed linear spaces (such as L1, L2, and C). We will study minimax approximation and the construction of good approximations (the exchange algorithm). We will also study orthogonal polynomials and least squares approximation. The results and techniques from approximation theory and numerical analysis will be applied in both the continuous and the discrete cases. The theory will be illustrated mainly by considering numerical approximation techniques by polynomials and splines.
More information can be found at http://www.maths.lu.se
Closed for applicationsApplication opportunities
Mathematics (Faculty of Engineering)
Sölvegatan 18, 223 62 Lund
Box 118, 221 00 Lund
Requirements and selection
Knowledge equivalent to the courses MATB21 Analysis in Several Variables 1, 7.5 credits, MATB22 Linear Algebra 2, 7.5 credits, MATB23 Analysis in Several Variables 2, 7.5 credits, NUMA01 Computational Programming with Python, 7.5 credits, and NUMA41 Numerical Analysis, basic course, 7.5 credits, are required.
Seats are allocated according to: Previous college/university studies (APAV): 100 %.
English language requirements
Most of Lund University’s programmes require English Level 6 (unless otherwise stated under 'Entry requirements'). This is the equivalent of an overall IELTS score of 6.5 or a TOEFL score of 90. There are several ways to prove your English language proficiency – check which proof is accepted at the University Admissions in Sweden website. All students must prove they meet English language requirements by the deadline, in order to be considered for admission.
How to apply
Lund University uses a national application system run by University Admissions in Sweden. It is only possible to apply during the application periods.
Step 1: Apply online
- Check that you meet the entry requirements of the programme or course you are interested in (refer to the section above on this webpage).
- Start your application – go to www.universityadmissions.se where you create an account and select programmes/courses, during the application period.
- Rank your programme/course choices in order of preference and submit them before the application deadline.
Step 2: Submit documents
- Read about how to document your eligibility and how to submit your documents at www.universityadmissions.se. Follow any country-specific document rules for Master's studies or Bachelor's studies.
- Get all your documents ready: official transcripts and high school diploma (Bachelor's applicants), official transcripts and degree certificate or proof of expected graduation (Master's applicants), passport/ID and proof of English proficiency (all applicants).
- Prepare programme-specific documents if stated in the adjacent column on this webpage.
- Upload or send all required documents to University Admissions before the document deadline.
- Pay the application fee (if applicable – refer to the section below on this webpage) before the document deadline.
*Note that the process is different if you are applying as an exchange student or as a part of a cooperation programme (such as Erasmus +).
*If you have studied your entire Bachelor's programme in Sweden and all of your academic credits are in Ladok, you do not have to submit transcripts or your diploma when applying for a Master's programme. However, there may still be other documents you need to submit! See the link below.
*Svensk student? Läs instruktionerna om att söka till ett internationellt masterprogram på lu.se.
Full programme/course tuition fee: SEK 18 125
First payment: SEK 18 125
Citizens of a country outside of the European Union (EU), the European Economic Area (EEA) and Switzerland are required to pay tuition fees. You pay one instalment of the tuition fee in advance of each semester.
EU/EEA citizens and Switzerland
There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.
If you are required to pay tuition fees, you are generally also required to pay an application fee of SEK 900 (approximately EUR 100) when you apply at www.universityadmissions.se. You pay one application fee regardless of how many programmes or courses you apply to.
Read more about paying the University Admissions in Sweden application fee and exemptions on the University Admissions website.
*Note that there are no tuition or application fees for exchange students or PhD students, regardless of their nationality.
Scholarships & funding
Lund University Global Scholarship programme
The Lund University Global Scholarship programme is a merit-based and selective scholarship targeted at top academic students from countries outside the EU/EEA.
Swedish Institute Scholarships
The Swedish Institute offers scholarships to international students applying for studies in Sweden at Bachelor's, Master's, PhD and post-doctoral levels.
Country-specific scholarships and funding options
Lund University has agreements with scholarship organisations and funding bodies in different countries, which may allow applicants to apply for funding or scholarships in their home countries for their studies at Lund University.
- Scholarships/funding for students from Brazil, Indonesia, Mexico, Colombia, Russia and Chile
- US student finance
- Canada student finance